Evaluate the Integral

Question

Evaluate  .

Question options:

1)	sin-1(x5) + C
2)	cos-1(5x) + C
3)
4)	The antiderivative cannot be found

Answer 1

To evaluate this integral we use substitution: t = x⁵

Then dt = 5x⁴dx, and = ∫dt/sqrt(1 - t²) = sin^-1t + C = sin^-1t + C = sin^-1(x⁵) + C.

Answer is 1)