What is the integral of \sqrt[5]{x+1} ?

The integral of \sqrt[5]{x+1} is 5/6 (x+1)^{6/5}+C

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integral of \sqrt[5]{x+1}

\frac{5}{6} (x + 1)^{\frac{6}{5}} + C

Solution steps

Apply u-substitution

Apply the Power Rule

: \frac{5}{6} u^{\frac{6}{5}}

= \frac{5}{6} u^{\frac{6}{5}}

Substitute back

u = x + 1

= \frac{5}{6} (x + 1)^{\frac{6}{5}}

Add a constant to the solution

= \frac{5}{6} (x + 1)^{\frac{6}{5}} + C

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What is the integral of \sqrt[5]{x+1} ?
The integral of \sqrt[5]{x+1} is 5/6 (x+1)^{6/5}+C