Question

Integrate: [x/sqrt(1+x)]dx

Answer 1

did you try letting u=ugly stuff

Answer 2

the ugly stuff being sqrt(1+x)

Answer 3

\[u=\sqrt{1+x} => u^2=1+x => 2 u du=dx => 2 du=\frac{dx}{u}=\frac{dx}
{\sqrt{1+x}}\]
So we have
\[\int\limits_{}^{} ( u^2-1) 2du\]

Answer 4

I replaced dx/sqrt(1+x) with 2 du

Answer 5

and i replace x with u^2-1 since we had u^2=1+x

Answer 6

\[2(\frac{u^3}{3}-u)+C\]
now just replace u with sqrt(1+x) and you will be done :)

Answer 7

thanks very much:)