Find the value of undefinite integral Find 
$$\int \frac{dx}{(x+1)^{1/2}+(x+1)^{1/3}}$$
I have tried with let $u=(x+1)^{1/2}+(x+1)^{1/3}$ but I have nothing to solve that undefinite integral. please give me a clue for solve it.

Use the substitution $u=x+1,$ and then $s=^6\sqrt{u}$ to get
\begin{equation*}
6\int \frac{s^3}{s+1}.
\end{equation*}
This is the same as 
\begin{equation*}
6\int (s^2-s-\frac{1}{s+1}+1)ds.
\end{equation*}
Integrate each term and re-substitute. 
