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

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

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

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

Solution steps

Apply u-substitution

Apply the Power Rule

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

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

Substitute back

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

Add a constant to the solution

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

\int (\frac{1}{x ^{8}}) d x

\frac{d}{d x} (25 - x)

x \to 0 lim (2 x + 1 - 1)

f^{^{'}} (x) = - cos (x)

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