What is the integral of e^x(1+e^x)^7 ?

The integral of e^x(1+e^x)^7 is ((1+e^x)^8)/8+C

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integral of e^x(1+e^x)^7

\int e^{x} (1 + e^{x})^{7} d x

\frac{( 1 + e ^{x} ) ^{8}}{8} + C

Solution steps

\int e^{x} (1 + e^{x})^{7} d x

Apply u-substitution

: \int (1 + u)^{7} d u

= \int (1 + u)^{7} d u

Apply u-substitution

: \int v^{7} d v

= \int v^{7} d v

Apply the Power Rule

: \frac{v ^{8}}{8}

= \frac{v ^{8}}{8}

Substitute back

= \frac{( 1 + e ^{x} ) ^{8}}{8}

Add a constant to the solution

= \frac{( 1 + e ^{x} ) ^{8}}{8} + C

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What is the integral of e^x(1+e^x)^7 ?
The integral of e^x(1+e^x)^7 is ((1+e^x)^8)/8+C