Trig substitution integration: x=a*tanθ, calculus 2

Integral by trig substitution, calculus 2, tangent substitution, 4 examples, calculus tutorial,

0:00 When do we use x=a*tanθ
0:31 Integral of 1/(a^2+x^2)
3:42 Integral of 1/(x^3+x)
8:20 Integral of sqrt(1+x^2)/x *hard*
15:18 How you should be practicing integrals
15:56 Integral of 1/(9+x^2)^(3/2)

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This channel is dedicated to students who are taking AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Feel free to leave calculus questions in the comment section and subscribe for future videos. #calculus #blackpenredpen

[wuyqrbt]

I just finished your last video.
And now you uploaded it .... Great

[MathAdam]

0:45 If you don't have the square root, you can still use it.
0:48 Maybe

[ShiroiTensh]

Crucial question: in 3rd integral
1. How do we deal with absolute value (from square root)
2. Why can't we cancel 1/tg with one secand; end up with sec^2*csc sub tg^2+1 end up with 2 integrals 1st of tg^2*csc equal to sin/cos^2 and u sub ad 2nd integral is just of csc

[CarlosCavasRodríguez]

In the first integer you can just use x=t/a but it is a good example although

[dyloniousmonk]

Could someone help me understand why we are able to make the cancellations at 11:03 ? Isnt that technically (sectan^2+sec)/tan ? How can we treat that as tan^2/tan and 1/tan ?

[coldszn]

If I pass this math class, I’m gonna gift you another poke ball speaker

[georgesadler]

Professor Black Pen Red Pen, thank you for the video. A Constant of Integration is needed after the integration is performed. Please correct this error in the video.

[wuyqrbt]

There is a big problem;
What about, as always, *that's it* ?!!

[ayushivarma]

I request to you sir please teach us in Hindi🗿📝📝📝📝