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

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

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

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

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

Solution steps

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

Apply u-substitution

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

Apply u-substitution

= \int v^{7} d v

Apply the Power Rule

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

Substitute back

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

Add a constant to the solution

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

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