What is the integral of 1/(\sqrt[1+3]{1+x)} ?

The integral of 1/(\sqrt[1+3]{1+x)} is 4/3 (1+x)^{3/4}+C

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integral of 1/(\sqrt[1+3]{1+x)}

\frac{4}{3} (1 + x)^{\frac{3}{4}} + C

Solution steps

Simplify

Apply u-substitution

Apply the Power Rule

: \frac{4}{3} u^{\frac{3}{4}}

= \frac{4}{3} u^{\frac{3}{4}}

Substitute back

u = 1 + x

= \frac{4}{3} (1 + x)^{\frac{3}{4}}

Add a constant to the solution

= \frac{4}{3} (1 + x)^{\frac{3}{4}} + C

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What is the integral of 1/(\sqrt[1+3]{1+x)} ?
The integral of 1/(\sqrt[1+3]{1+x)} is 4/3 (1+x)^{3/4}+C