Question

Indefinite integral wrt x of x sqrt(1+x)?

Answer 1

2/5*(x + 1)^(5/2) - 2/3*(x + 1)^(3/2) + C

substitute u = 1 + x

Answer 2

\[\int\limits_{}^{}x*\sqrt{x+1} dx\]
let u=x+1
du=1 dx
if u=x+1, then u-1=x
\[\int\limits_{}^{}(u-1) \sqrt{u} du\]
=\[\int\limits_{}^{}(u^{1+\frac{1}{2}}-u^\frac{1}{2} )du\]
\[\int\limits_{}^{}(u^\frac{3}{2}-u^\frac{1}{2})du\]