What is the integral from 0 to ln(2) of e^x(1+e^x)^3 ?

The integral from 0 to ln(2) of e^x(1+e^x)^3 is 65/4

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integral from 0 to ln(2) of e^x(1+e^x)^3

\int_{0}^{l n (2)} e^{x} (1 + e^{x})^{3} d x

\frac{65}{4}

Decimal

16.25

Solution steps

\int_{0}^{l n (2)} e^{x} (1 + e^{x})^{3} d x

Apply u-substitution

: \int_{2}^{3} u^{3} d u

= \int_{2}^{3} u^{3} d u

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{2}^{3}

= [\frac{u ^{4}}{4}]_{2}^{3}

Compute the boundaries:

\frac{65}{4}

= \frac{65}{4}

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What is the integral from 0 to ln(2) of e^x(1+e^x)^3 ?
The integral from 0 to ln(2) of e^x(1+e^x)^3 is 65/4