What is the integral of (4+e^x)^2e^x ?

The integral of (4+e^x)^2e^x is ((4+e^x)^3)/3+C

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integral of (4+e^x)^2e^x

\int (4 + e^{x})^{2} e^{x} d x

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

Solution steps

\int (4 + e^{x})^{2} e^{x} d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = 4 + e^{x}

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

Add a constant to the solution

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

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What is the integral of (4+e^x)^2e^x ?
The integral of (4+e^x)^2e^x is ((4+e^x)^3)/3+C