What is the integral of \sqrt[3]{x+a} ?

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

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integral of \sqrt[3]{x+a}

\int 3 x + a d x

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

Solution steps

\int 3 x + a d x

Apply u-substitution

: \int 3 u d u

= \int 3 u d u

Apply the Power Rule

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

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

Substitute back

u = x + a

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

Add a constant to the solution

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

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