Question

How to find the primitive of `sqrt(x)e^(xsqrt(x))`?

Answer 1

`int sqrtxe^(xsqrtx ) dx = 2/3 e^(x sqrtx)+C`

Explanation:

Substitute `sqrt x = t`, `x=t^2`, `dx=2tdt`:

`int sqrtxe^(xsqrtx ) dx = 2int t^2e^(t^3)dt = 2/3 int e^(t^3)d(t^3) =2/3 e^(t^3)+C = 2/3 e^(x sqrtx)+C`