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

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

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

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

Solution steps

Apply u-substitution

Apply the Power Rule

: \frac{3}{2} v^{\frac{2}{3}}

= \frac{3}{2} v^{\frac{2}{3}}

Substitute back

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

Add a constant to the solution

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

n = 0 \sum \infty 2 \cdot 0. 3^{n}

\frac{d y}{d x} + x (y^{2} + y) = 0

\int \frac{2 tan ( x )}{1 - tan ^{2} ( x )} d x

\frac{d}{d x} (tan (2 x + 1))

y = x^{3} + 6 x

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