Question

Evaluate the following integral: ∫1/((x²+1)√x)dx

\(\int\frac{1}{(x^2+1)\sqrt{x}}\)dx

Answer 1

Given,

∫1/((x²+1)√x)dx

let x = t² 

dx = 2t dt

\(\int\frac{2dt}{t^4+1}\)

Dividing by t² in both numerator and denominator,