# How to solve this root integral

#### transgalactic

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
??

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#### tiny-tim

Homework Helper
$$\int \frac{1-\sqrt{x+1}}{1+\sqrt[3]{x+1}}$$
Hi transgalactic!

Hint: substitute!

#### transgalactic

i tried t=(x+1)^1/3
but it creates anoted roots in the dt
??

#### tiny-tim

Homework Helper
i tried t=(x+1)^1/3
but it creates anoted roots in the dt
??
uhh?

dx = … ?

anyway, (x+1)1/6 might be easier.

#### transgalactic

but i dont have members of 1/6 power
??

#### Mark44

Mentor
Sure you do. a^(1/2) = a^(1/6)^3, and b^(1/3) = b^(1/6)^2.

"How to solve this root integral"

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