How to solve this root integral

i tried this:
\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}=\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}*\frac{1+\sqrt{x+1}}{1+\sqrt{x+1}}*\frac{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}{1-\sqrt[3]{x+1}+(x+1)^{\frac{3}{2}}}
but when i got read of 2 roots i got another two roots which are more complicated
i tried t=(x+1)^1/3
but it creates anoted roots in the dt


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but i dont have members of 1/6 power
Sure you do. a^(1/2) = a^(1/6)^3, and b^(1/3) = b^(1/6)^2.

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