Integration Problem?

Question

Any math whizzes able to find the integral of (x+x^(3/2))^(-1/2)? If using substitution, what value do you use for u?

Answer 1

Integrate 1/√[x + x^(3/2)] with respect to x.

∫{1/√[x + x^(3/2)]}dx

Let
u² = x
2u du = dx

∫{2u/√[u² + u³]}du = ∫{2u/[u√(1 + u)]}du = ∫{2/√(1 + u)}du
= 4√(1 + u) + C = 4√(1 + √x) + C

Answer 2

[4([x^3/2]+x)^1/2]/([x^1/2]