Question

Trigo sub. Integral

Answer 1

let x as 2a tan^2 theta

Answer 2

it was written in the book

Answer 3

yes, that looks like a good substitution
where are you stuck ? :)

Answer 4

\(\large x=2a\tan^2\theta \)
\(\large dx=4a\tan\theta \sec^2\theta ~d\theta \)

the integral becomes :
\[\large \int \dfrac{4a\tan\theta \sec^2\theta ~d\theta }{2a\tan^2\theta \sqrt{2a(2a\tan^2\theta ) + (2a\tan^2\theta)^2 }}\]

Answer 5

simplify as much as you can ^^

Answer 6

Thank you. I'll give you the answer later.. i'll just simplify this.

Answer 7

okay :) just want you notice that the stuff inside sqrt can be written as : \(4a^2\tan^2 \theta \sec^2\theta \)