Integration into Inverse trigonometric functions using Substitution

Рет қаралды 779,199

7 жыл бұрын

This calculus video tutorial focuses on integration of inverse trigonometric functions using formulas and equations. Examples include techniques such as integrating by substitution, u-substitution, splitting fractions and completing the square. This video contains plenty of practice problems of integrating inverse trig functions.
Arc Length Problems:
• Arc Length Calculus Pr...
Surface Area Problems:
• Surface Area of Revolu...
Work Problems - Calculus:
• Work Problems - Calculus
Integration By Parts:
• Integration By Parts
Tabular Method:
• Integration By Parts -...
_______________________________
Trigonometric Integrals:
• Trigonometric Integrals
Trigonometric Substitution:
• Trigonometric Substitu...
Integration By Partial Fractions:
• Integration By Partial...
Trapezoidal Rule:
• Trapezoidal Rule
Simpson's Rule:
• Simpson's Rule & Numer...
________________________________
Improper Integrals:
• Improper Integrals - C...
Integration Into Inverse Trig:
• Integration into Inver...
Integration of Rational Functions:
• Integration of Rationa...
Integral of Logarithmic Functions:
• Integral of Logarithmi...
Integrating Exponential Functions:
• Integrating Exponentia...
__________________________________
Calculus Final Exam and Video Playlists:
www.video-tutor.net/
Full-Length Videos and Worksheets:
/ collections

Пікірлер: 225

@TheOrganicChemistryTutor Жыл бұрын

Next Video: kzfaq.info/get/bejne/at96oMuLp6iYYKs.html Final Exams and Video Playlists: www.video-tutor.net/

@alvinpetina3466 7 жыл бұрын

May you live long! for the sake of Engineering students. Thank you

@Integrelle 6 жыл бұрын

LITERALLY!!! We were just taught the basic arctan formula in my engineering calc class, but no examples!! THIS SAVED me hours!

@brandons1095 4 жыл бұрын

Not just engineering, AP AB Calculus students thank you to infinity. You have saved many grades

@jairajsha8208 3 жыл бұрын

@@brandons1095 yes we thank you lim n-->∞

@chriswiddajonathan8941 3 жыл бұрын

youre from the balut country, arent you? cant say i dont agree with you 1000% tho

@gabrielmakoi3905 3 жыл бұрын

Amen for him

@whitegoodmantrades8720 4 жыл бұрын

I promised myself if I got an A in Calc this semester I would order a hoody. Thanks to you, my hoody is on its way! You’re a life saver!

@oliversmith4986 4 жыл бұрын

I just wanted to take a moment to thank you, man. You've changed so many peoples lives by helping them. You seem like a great person, I wished I knew you in real life, but I don't sadly. Once again, thanks, man!

@bulelanisigcawu2322 2 жыл бұрын

THE ONE AND ONLY TUTOR THAT DOES NOT COMPLICATE THINGS FOR STUDENTS.I THANK YOU FOR THAT A LOT

@ChampChamp000 3 ай бұрын

Give some credits to Sal khan aswell 😒

@timschavusky 3 жыл бұрын

bro this guy the smartest human being i’ve ever encountered. cheers to you mate.

@planewire2153 6 жыл бұрын

its like the ghost of precalculus has paid me a visit today

@sonyawong6092 4 жыл бұрын

My teacher got me looking through my textbook like a madman. You simplified it just like that. Mind blown. I'm always grateful for your videos. Please keep it up!

@callmekaymusic 5 жыл бұрын

thanks brother with your calm voice... makes me believe I will not fail lol haha

@Xenderz 4 жыл бұрын

I GOT PERFECT IN MY EXAM BECAUSE OF YOU! THANKYOU!

@LootLust 4 жыл бұрын

Had you been around 10 years ago, I probably would have stayed in college. With that lapse in time between then and now, you are a godsend and make Calculus 2 fun again. Thank you for your service to college students everywhere!

@jimhalpert9803 4 жыл бұрын

Why are you watching if you're not in college or studying?

@LootLust 4 жыл бұрын

@@jimhalpert9803 just because I didn't stick it out the first time around doesn't mean I can't go back and try do it again... or is that a foreign concept to you?

@jimhalpert9803 4 жыл бұрын

@@LootLust Why are you being so aggressive? I was just curious and wanted to know if you liked integrals in general or if you were just passionate about learning maths.

@LootLust 4 жыл бұрын

@@jimhalpert9803 lol. Totally misread the tone of your first comment. It came off smart-assy. I do enjoy math a fair amount, but at the time I was taking Calc 2 again.

@jimhalpert9803 4 жыл бұрын

@@LootLust haha lol when I read my first comment , it sounds like I'm questioning why you're studying in the first place. Good thing you're interested in maths. Good luck!

@emmam9269 4 жыл бұрын

you got me through 2 years of calc and I'm sure more in the future thank you so much man

@puterimalaysia9 5 жыл бұрын

Its just awesome to search something and your vids come up. Sooo helpful. Love you!

@agirlwholikesboyz 6 жыл бұрын

Thank you so much I watch your videos every time I have homework. I am so blessed and grateful to have found you.

@danielcervini2545 Жыл бұрын

Thank you for this content! If everyone was more like you, the world would be a better place.

@SuperShana97 5 жыл бұрын

I feel like you make these a lot easier than my professor

@user-ys2de2be9b 4 ай бұрын

Professors are useless

@nicholaseiswert5265 3 жыл бұрын

thank you so much for everything. learning calculus online this year is terrible but your videos always help me learn new material.

@lordfranktex5270 3 жыл бұрын

Thanks man for sharing this knowledge....calculus seems very easy with your videos. Thanks once again.

@ChideraUwandu 6 жыл бұрын

Thank you so much. Always feel more ready for a math test afterwards.

@ludypalacios2889 4 жыл бұрын

May you be willing to do a video about hyperbolic functions and their inverse?

@lauraa5921 3 жыл бұрын

Legend, life saver, ultimate teacher. Thank you.

@waleedbro9117 2 жыл бұрын

Words are not enough to describe my gratitude for your works

@deetyareddy3874 Жыл бұрын

Sir, generations to come will benefit from such videos 🙏 we owe our careers to you, sir. Thank you so much sir 🙏

@kabirzama5854 5 жыл бұрын

Thanks, this really helped with my studying

@samarthsubbaraomullapudi7304 3 жыл бұрын

You re one of the best teacher - May god bless ( soon I want to contribute to your efforts)

@lycaarroyolariosa7172 2 жыл бұрын

Thank you so much! On my 2nd yr in Eng., I went here coz I feel helpless. You have taught me a loooot. Thsm!

@palermojohncarlov.8891 4 жыл бұрын

Thanks bro for sharing your knowledge to everyone, it really helps me to understand reverse trigonometric integration.. Good job for the clear and clean execution of the topic,thumbs up😁😁😁

@elifderbentli9370 3 жыл бұрын

THEY MAKE IT SO CONFUSING IN THE TEXTBOOK WITH PROBABLY 5 ROUNDS OF SIMPLIFYING IN ORDER TO GET THE ANSWER

@user-ml1jp9dw7n 6 ай бұрын

Today is our final term examination for integral calculus. Thank you for your videos that helps and contribute in my understanding in this subject ❤, God bless you more!

@musicalmyranda2636 5 жыл бұрын

This was very helpful. Thank you

@davidschumm9936 2 жыл бұрын

idk how the id get through calculus without you!

@stoffel89 7 жыл бұрын

in 19: 42 you have a solution to the problem. but will the problem also be correct if you use the same u substitution for both integrals, thus getting the answer 1/2 ln (u) - 3ln(u) + c? or must you always apply the the rules to each integral separately? thus you must apply arc tan rule at the second part of the integral?

@YourMomsHouseBih 4 жыл бұрын

You make it seem so simple!!!

@mahmoudwagdy4936 5 жыл бұрын

Thank you so much....keep on rising!.

@jelome_x 3 жыл бұрын

You are definitely one of the best Math instructor I've come across on KZfaq. You're a life saver. I really do enjoy and understand your videos. Very explicit. More grace to you. God bless you man.

@nathanburns3487 5 жыл бұрын

Very helpful! Thanks a lot!

@georgesadler7830 10 ай бұрын

Professor Organic Chemistry Tutor, thank you for an outstanding video/lecture on Integration into Inverse Trigonometric Functions using Substitution. Integration into Inverse Trigonometric Functions ranges from simple to complex, however pattern recognition also helps when computing these complex Integrals in Calculus. This is an error free video/lecture on KZfaq TV with the Organic Chemistry Tutor.

@Kerry. 3 жыл бұрын

Thank you! Integrals through me through a loop but your videos didn't!

@emilymoomey2081 5 ай бұрын

THANK YOU SOOOO MUCH!!! THIS IS SO MUCH SIMPLER THAN I THOUGHT

@JoseChavez-eh4jx 5 жыл бұрын

This guy is a mathematical genius!!!

@user-sg6go6mq1v 3 жыл бұрын

Thanks very much for your work.... we ask if you can make a video about the integration of hyperbolic and inverse hyperbolic functions.

@lovelygelly 3 жыл бұрын

Thank you for making me pass my calculus tests

@chifumujere3243 2 жыл бұрын

Superb and benefited from the well articulated easy explainory

@milessmiles65 4 жыл бұрын

Do you have any examples with the actual finite integrals with number ranges

@yoookapathis1996 5 жыл бұрын

Hi is completing the square that taking half is effective to all equation regarding to the equation problem? If not what should do aside taking half of midle of equation?

@clayjoiner2581 4 жыл бұрын

Hey so at 13:50 why if you have (x/x^2+1) did you have the whole denominator U instead of applying the arctan formula? X^2 is U^2 and 1 is a^2. Also as everyone else says you are the goat at math.

@ghazalehrahimi432 3 жыл бұрын

that's exactly my problem too! -_-

@roelandkramer4302 3 жыл бұрын

I think it's because when u^2 = x^2, u = x, du = dx. Therefore you will not to be able to let the numerator (x) disappear, and get the integral in the right form. If u^2 would have been x^4, it would have been another story since then you can multiply by du/2x. (like an example in the vid)

@johnr1875 6 жыл бұрын

im sure this is obvious, but why are we only using the principle square root? Is it because of the domain of the function? If so, then can't one of the terms, like the x term, be negative?

@mineralwater7321 2 жыл бұрын

Thank you so much for helping me to pass my calculus 2

@dreivonfunf9489 Жыл бұрын

Thank you so very much for this video!

@kateherod7536 Жыл бұрын

Thank you this helped tremendously!

@gabrielmakoi3905 3 жыл бұрын

May God continue to keep you for us, your students.

@hiro6406 4 жыл бұрын

What. Why is this so easy compared to what my prof taught??? Test is 6 hours later and I only stumbled across this now. F the notes, i will just watch you instead. Thank YOUUUUU

@lalisaprotector6984 6 жыл бұрын

Thank you so much! 😭💖

@johnpaulcaraan1438 6 жыл бұрын

Thanks! It's a big help because we have a quiz later.

@ahmedalagib5312 4 жыл бұрын

somebody get this man a wider screen !!!

@noureddineakli6862 3 жыл бұрын

thanks so much for you efforts god bless you

@JohnDoe-jz9zy Жыл бұрын

Imagine one day this guy woke up and had the massive realization that he was going to make the lives of millions a million times easier.

@celin3598 Жыл бұрын

bless your beautiful soul. seriously dude, thank you.

@johnphiliposman6542 Жыл бұрын

31:30 can also use natural log formula du/u since the 2 terms in the denominator are perfect squares, so it will become xdx / 5 - (x² - 4) or -x² + 9.. we can let u = -x² + 9 and du = -2x dx, and dx = du/ -2x... We now have integral of x du/-2x in the numerator, we can cancel x then put the constant -1/2 outside so we now have -1/2 integral of du/u which is just -1/2 ln | -x² + 9 | + c

@mohammadhamza232 6 жыл бұрын

These questions can also be solved using trigonometric substitution, I'm getting a little confused please can someone tell me when we'll use trigonometric substitution and when this inverse thing

@thomascruickshank7407 5 жыл бұрын

Mohammad Hamza bro I was thinking the same thing

@rajthomas4224 4 жыл бұрын

@@thomascruickshank7407 Bro I was thinking the same thing. Currently in Calc 2

@shiroyukisnow 4 жыл бұрын

correct me if i am wrong, but i think you can use this method if the functions are in the denominator, while in trig substitution, the functions are in the numerator or there is simply no denominator.

@meenakshimarketing6503 4 жыл бұрын

To state the truth you can actually do it by any method because integration doesn't have discrete methods like differentiation 😊

@somtonwadiaro8076 2 жыл бұрын

@mohammed aswr. Its confusing. Dunno when to use either of them

@tomcat9761 3 жыл бұрын

Damn you made my Computer Science life so easy

@tx5648 2 жыл бұрын

will you please make a video about hyperbolic functions like sinh and cosh and those formulas ;-; thank you for everything

@jaylencalinaw1080 3 жыл бұрын

I just found out that my professor used the exact same expression from *THIS VIDEO* I have been looking for a solution to for the past 12 hours. On cloud nine. Thank God I have internet connection and KZfaq.

@kleodavelajarca7479 5 жыл бұрын

THANK YOU SO MUCH DUDE!

@kelvinjack6268 4 ай бұрын

😶🤐... I wish I could leave a comment as impressive as your teachings have been. God bless you sir 😊

@rachelhiltystudenthbhs2575 Жыл бұрын

the hero we never knew we needed

@user-gl8hf6ts8t 10 ай бұрын

You are truly the best❤

@davidearlsantos5628 5 жыл бұрын

Tip: When you derive x^n and the equation is ×dx/something you could simply over the derivative of it with only just the number so it will be xdx=du/n. No need to bring the x so there will be no cancellation.

@ThOtherzz_ 4 жыл бұрын

On the last problem, should it be on radian, or degree mode? Cause i thought it should be on degree mode.. 🤔

@camilahleclere5419 3 жыл бұрын

you're so awesome, thank you so much !!!

@stevengallego7332 12 күн бұрын

6:05 is it ok to cancel out the 2 even if they are both denaminator?

@hhkk1253 6 жыл бұрын

Thanks for you very much my love. ..... lam girl from London

@gjinkalla7121 5 жыл бұрын

Caleb Frank omg bless me too i have a bombass exam in 1 week 😭

@oscarmlotshwa5091 4 жыл бұрын

you are the best man long live

@shawaixaaquey8316 2 жыл бұрын

Greatest tutor Greatest tutor

@jcnotnot8120 5 жыл бұрын

28:35 what happens to a^2 when you take dz?

@Nemoguzapomnit 5 жыл бұрын

The same as it would be any constant. d/dx of a constant is equal to 0

@Rickmanou81293 6 жыл бұрын

Where did your 2a go at 28:42 when taking the Dz?

@Wilson-si6jr 6 жыл бұрын

Cody Rickman Pretty sure you figured it out but a squared is a constant meaning it will disappear once you derive the function.

@mustafamalik4211 6 жыл бұрын

I have a question. Are we allowed to use Partial fractions instead of using inverse tan?

@Iforonlyif 6 жыл бұрын

No, because (a^2)+(b^2) is not factorable (I'm 98% sure)

@mohubeduabram3896 6 жыл бұрын

NO we can only use partial fraction when the degree of the denominator is grater than the degree of the numerator.

@brydust 6 жыл бұрын

Mohubedu Abram you could first perform long division then you can do partial fraction decomposition

@lelenovo6296 4 жыл бұрын

Thank you master!

@Mathicalminds 2 жыл бұрын

Enjoying your video 🔥❤️

@user-jf7ge4io4r 5 жыл бұрын

I love your voice very much🙏🙏

@ksfishchannel 5 жыл бұрын

You're a gee dee saint, man.

@kkkkkunn 6 жыл бұрын

there are somethings that u forgot to apply just like 1/a at 31:01 in this video, but it's alright u r a legend

@kkkkkunn 6 жыл бұрын

the answer must be 3/2 arctan x+3/ 2 + c (the 2nd term of the answer)

@jackspicer455 3 жыл бұрын

This guy is a Genius

@hemmarajkanesan6881 8 ай бұрын

i just wanted to ask, should we ignore the negative symbols?

@shwunhlaing104 Ай бұрын

can someone tell me if I can solve w/o the u-substitution??

@jonahlaing4379 2 жыл бұрын

you are a blessing.

@bernadettegumop-as5389 3 жыл бұрын

How I wish you were my professor. 🥺

@alvinbensongocheco612 4 жыл бұрын

Thank you the man the legend

@unorclowiejoyflores858 3 жыл бұрын

Belated Happy Teacher's Day Organic Chem 👍

@gerardtyson2274 Жыл бұрын

There are also inverse hyperbolic substitution formulas; arccosh, arcsinh, arcsech, arctanh

@ainomugishaandrew2795 2 жыл бұрын

Good job bro💪

@mckintoshtudee7336 6 жыл бұрын

thanks a lot man

@lilikajenkins344 Жыл бұрын

you are SAVING ME

@raratarawneh3087 6 жыл бұрын

Thank you ⚘⚘

@user-vy4zy5sn2x 8 ай бұрын

Bro goated af, thank you

@Nemoguzapomnit 5 жыл бұрын

Thx for that great video! Btw in the last problem I substituted U with x-3 and got the same answer but still pluged 3 and 0. Is it ok?

@mergmendoza7641 5 жыл бұрын

Thank u sir!! I hope I can pass my exam tomorrow!!

@jastinloydsalaya2064 Жыл бұрын

thank you very much

@gurj0tb Жыл бұрын

this man deserves some flowers.

@bluebraintech4168 2 жыл бұрын

good job

@JuanGonzalez-fn4uf 6 жыл бұрын

Question: would [ (x^2+1)/2 -(ln(x^2+1))/2 + C ] be an acceptable answer for the problem at 11:55. I did it a bit different.

@shwetaporwal6782 2 жыл бұрын

I got the answer in arctan