What is the integral of e^x\sqrt[3]{e^x+2} ?

The integral of e^x\sqrt[3]{e^x+2} is 3/4 (e^x+2)^{4/3}+C

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integral of e^x\sqrt[3]{e^x+2}

\int e^{x} 3 e^{x} + 2 d x

\frac{3}{4} (e^{x} + 2)^{\frac{4}{3}} + C

Solution steps

\int e^{x} 3 e^{x} + 2 d x

Apply u-substitution

: \int 3 u + 2 d u

= \int 3 u + 2 d u

Apply u-substitution

: \int 3 v d v

= \int 3 v d v

Apply the Power Rule

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

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

Substitute back

= \frac{3}{4} (e^{x} + 2)^{\frac{4}{3}}

Add a constant to the solution

= \frac{3}{4} (e^{x} + 2)^{\frac{4}{3}} + C

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What is the integral of e^x\sqrt[3]{e^x+2} ?
The integral of e^x\sqrt[3]{e^x+2} is 3/4 (e^x+2)^{4/3}+C