Trig Subs | How To Choose The Substitution & Deal With Indefinite Integrals

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Instead of guessing or memorizing what trigonometric substitution to use, I'll walk through how I anticipate what is the best trig sub to use. In this example it will be an indefinite integral, and that poses its own set of problems. We have to be careful about our restriction on the domain as before, but now we have to back solve the final answer to put it in terms of the original variables. This involves a bit of trigonometry.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. #calculus #math

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There is an error at 4:43. It should be

gentlemandude

Corrent answer is:

atan(x/2) x
+ + C.
16 32 + 8x^2

Thanks for video.

ОрландоОрсо

Thank you sir u uploaded the video, when Im going to trig sub lecture tomorrow it will be a great preview for me. Appreciate your effort sir! Keep it up!

nsy

I was struggling at this for a whole week and you saved my life and possibly my grade! Let's see how Monday goes I might actually pass this class. I have the lowest rated professor in my college😭😭

lordfarquaadreal

I don’t know if it helps because it’s not EXACT but I thought it was curious how the forms needed coincide (loosely) with the arctrig derivative: like d/dx arctan is 1/1+x^2 and when we see a^2+x^2 we sub x for atan(theta) thats how I remember which one I need anyway

mmariokart

If x can take on any real value, then the integral has to exist for any real value of x, so it's really important to pick a function like tan that can take on any value when we substitute x with it. Furthermore, it's very important that we pick a domain for the new independent variable θ, so that our function that we substituted x with will be able to properly exist for the same value of x, and be "one to one" just like x

naiko

Great vídeo! I just have a question... It is "ok" to define the tangent between -Pi/2 and Pi/2? It shouldn't be undefined exactly at these limits?

AangContreras

Is sinx = x a trig substitution? (It’s a joke haha)

duckymomo

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