Find : ∫√x/√(a^3-x^3)dx​

Question

Find : \(\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx\)

Answer 1

We have,

I = \(\int\frac{\sqrt x}{\sqrt{a^3-x^3}}dx\) 

  = \(\int\frac{x^{1/2}\,dx}{\sqrt{a^3-x^3}}\)