Yes, I'm fairly certain that is a standard integral, and it comes out to:
sin^{-1}y + C
But I'm also fairly certain that I am supposed to solve this problem using the expression, substitution, and identity when I do the trig sub. Maybe I am overcomplicated the problem and should just stick to...
as in changing the bottom from 1 + (sinx)^2 to 1 + y^2 ?
I can get to:
\int \frac{sec^{2}\Theta d\Theta}{\sqrt{1+tan^{2}\Theta}}
But after that it makes no sense, I just get back to the original equation when I sub. again.
Homework Statement
\int \frac{cosx dx}{\sqrt{1 + sin^{2}x}}
Homework Equations
Expression: \sqrt{a^{2} + x^{2}}
Substitution: x = a*tan\Theta
Identity: 1 + tan^{2}\Theta = sec^{2}\Theta
The Attempt at a Solution
I have tried using Trig Substitution, but I end up getting an equation much...