
Trig substitution calc 2
Dear MHF experts (btw, you guys rock!! lol),
$\displaystyle \displaystyle \int \frac{x^2}{\sqrt{25x^2}}\,dx$
(someone else's calculations for this, last step is correct, i took the derivative and it equals the original integral)
let sin(θ) = x/5 ; 5 cos(θ) dθ = dx
= 25 ∫ sin²(θ) dθ
= 25/2 ∫dθ  25/2 ∫cos(2θ) dθ ............. sin²(θ) = (1/2) [1  cos(2θ)]
= 25/2 θ  25/2 sin(θ)cos(θ) + c
= 25/2 arcsin(x/5)  x/2 √(25  x²) + c

I got to the step in bold no problem. I got the first term in the last step right; however, I cannot seem get from the second term in bold to the second term in the last step. I only need help getting from the bold underlined to the last underlined term xD
In the last step that's underlined, I can substitute (x/5)=sinθ ... but cannot figure out what to substitute for cosθ

$\displaystyle sin \theta = x/5; cos ^2 \theta + sin ^2 \theta =1; cos \theta = \sqrt{1x^2/25}; cos \theta = 1/5 \sqrt{25x ^2}
$