Question

Evaluate using a trig sub:

Answer 1

\[\LARGE \int \frac{x^3}{\sqrt{1-x^2}}~dx\]

Answer 2

let x = sint
dx = cos dt
x^2 = sin^2
1-x^2 = cos^2
sqrt (1-x^2) = cos
plug all
integrand: sin^3 cos dt/cos= sin^3 = (1-cos^2) sin= sin-cos^2sin
the second term
let u = cos
du = -sin
it becomes -u^2du
I think you understand my short cut

Answer 3

whenever given \(\sqrt{1 - x^2}\) in the denom, your first approach should be subbing sin or cos.

Answer 4

Thank you guys :)