Integration using t=tanx

In this video, I showed how to integrate a rational function using the t=tanx substitution

[@jan-willemreens9010]

... Good day Newton, I have just one tiny comment at time 8:48: Why the u^2 + u in the denominator of the integrand instead of u^2 + 1? ... I know it is accidentally written ... Great presentation from your hand as always; I like these integrals full of surprises ... Take care, Jan-W

[@PrimeNewtons]

Oops! I noticed after uploading. I will pin your comment. Thank you, Jan-W.

[@user-ml2mg6vc1r]

Learning from you. I would suggest others to try solving the question by simplifying firstly the expression using the identity (sin^2+cos^2=1 --> sin^2 = 1-cos^2). I think this will save time.

[@nicholasbarinda]

Wow!!!!!, i had no idea to attempt this integral, thanks mr prime newtons, more blessings

[@AliMohamedsayed]

ur explaination is the best ever i thank u for everything u do thank u for ur help ❤❤

[@XolaMbusi]

It is tricky but you are explaining it very very good

[@B.r.y.t.o.n]

it was good the way you made things look easy but always start by showing us the reason why we choose to use that method of intergration

[@prollysine]

Hi, it's a magical task, the derivation of the first part is great. If we multiply by 1/(cosx)^2, we get (1/2) int (secx^2/(tanx^2+2))dx, and let t=tanx, (1/2)int (1/( t^2+2))dt and we can already write I=(1/(2sqrt2))*arctan(tanx/sqrt2) + C, Thank's

[@PrimeNewtons]

That's cool!

[@prollysine]

@@PrimeNewtons Thank's Prime Newtons, her presentations are exciting, understandable, we can supplement our knowledge ... The written t=tanx helped with the solution!

[@yessinegebssi162]

❤❤❤❤❤

[@Ni999]

👍

[@bigonhim14]

This is Great..😅

[@slowwindow4223]

Thank you sir, but I have a question at 8:08 why is it sqrt2 and not 2

[@ismaels3471]

its arctan derivative we need 1 / 1 + u^2 so we take the sqrt of 2 to obtain this form

[@dreamdayeofficial]

Here for your cap[hat]

[@crtlallaw]

that triangle is realy good way to get sin and cos my doctor didnt use that

[@varhaforsson9194]

In minute 8:47 your wrote u instead of 1 in the denominator

[@vismof]

what if i have in denominator tan or cot ?

[@deborahatobrah6827]

Boses