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

The integral of e^x(1+e^x) is ((1+e^x)^2)/2+C

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

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

\frac{( 1 + e ^{x} ) ^{2}}{2} + C

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = 1 + e^{x}

= \frac{( 1 + e ^{x} ) ^{2}}{2}

Add a constant to the solution

= \frac{( 1 + e ^{x} ) ^{2}}{2} + C

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What is the integral of e^x(1+e^x) ?
The integral of e^x(1+e^x) is ((1+e^x)^2)/2+C