What is the integral of e^x(1+e^x)^3 ?

The integral of e^x(1+e^x)^3 is ((1+e^x)^4)/4+C

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integral of e^x(1+e^x)^3

\int e^{x} (1 + e^{x})^{3} d x

\frac{( 1 + e ^{x} ) ^{4}}{4} + C

Solution steps

\int e^{x} (1 + e^{x})^{3} d x

Apply u-substitution

= \int u^{3} d u

Apply the Power Rule

= \frac{u ^{4}}{4}

Substitute back

u = 1 + e^{x}

= \frac{( 1 + e ^{x} ) ^{4}}{4}

Add a constant to the solution

= \frac{( 1 + e ^{x} ) ^{4}}{4} + C

What is the integral of e^x(1+e^x)^3 ?
The integral of e^x(1+e^x)^3 is ((1+e^x)^4)/4+C