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.

$$\begin{align*}
\int \frac{dx}{\left ( x+1 \right )^{1/2}+ \left ( x+1 \right )^{1/3}} &\overset{u^6=x+1}{=\! =\! =\! =\!}\int \frac{6u^5}{u^3+ u^2}\, du  \\ 
 &= \int \left ( 6u^2 - 6u - \frac{6}{u+1} + 6 \right )\, du\\ 
 &= u\left ( 2u^2-3u+6 \right )-6\log (u+1)
\end{align*}$$
Now substite $u$ with $\sqrt[6]{x+1}$ and add the constant and you are done. 
