Integral of 1/(1+x^2)

This calculus video tutorial explains how to find the integral of 1/(1+x^2) using trigonometric substitution.

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[RicJiang]

thanks this specific integral had me stummped, my calc 3 professor expected us to know this right off the bat

[syntherwilll]

Damn smoothest integration 1/1+x^2 proof online

[sharkronical]

tan(q) "Organic Chemistry" Tutor

[zemotika]

I just wish I was able to know this stuff without needing to reference a video or textbook… like how tf do people remember which identity you need… like how do you know to sub x for tan

[timnikitenko]

how do you know to replace x with specifically with tan u? if i got that question out of no where, why shouldnt i try plugging in... cos u or... sec u as x? how do i know that its tan u specifically?

[skylonace]

Thanks man, Straight to the point and useful. This really helps.

[alifrahman]

saved my ass before exam man, ur a legend, so simple yet so powerful

[lucalanzi]

I love how the Organic Chemistry Tutor never, ever, ever explains **why**. He just tells you what to do. jesus

[mayankmandloi]

How did you substitute x with tan2u and dx with sec2xdu

[Lalitamm]

@TheOrganicChemistryTutor could you use inverse trig for this question instead? if you rewrite it as integral 1/(sqrt1)^2+x^2 dx then use the inverse trig integral rule of integral 1/b^2+(ax)^2dx = 1/ab tan^-1(ax/b) + C? that will also give you the answer of tan^-1(x)+C which I feel like is much easier but is that illegal? lol

[anty.]

Could someone link me a video to trigonometric substitution? The link for it in the description doesn't work anymore, and I'm so confused how you get a trig function from just a rational expression.
I randomly got this question on an assignment with none of the other ones like this, but still dont know if I could get something like this on a quiz.

[raw]

Why do you specifically replace x with tan x

[luqmanulhakim]

can you tell me why x can be equal to tan u ? help me i need to explain about this in my class tomorrow

[braineedly]

why does x become tan u, why doesn't become cos u, sin u, cot u etc. why does x have to be tan u?

[PeterMek-ftpu]

Thank you....well explained and to the point..

[ninjayt]

Bro we can directly substitute tan^-1(x) it's a direct formula

[silentintegrals]

Great Video! Solving integrals is allways fun!

[VijayVindal]

Sir isme 1/x² ko logx formula lagakar kyun nhi kr skte

[QuinnBeckley]

why would you use trig when you don't need trig, this was painful

[paulinemureithi]

Thanks for the explanation but what if it had limits??