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

The integral from 0 to ln(2) of e^x(1+e^x)^2 is 19/3

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

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

\frac{19}{3}

Decimal

6.33333 \dots

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

\frac{19}{3}

= \frac{19}{3}

\int_{- 2}^{3} ∣ x - 1 ∣ d x

\int_{- \infty}^{3} e^{2 x} d x

\int_{a}^{b} (a x + b)^{p} d x

\int_{0}^{11} 121 - x^{2} d x

\int_{0}^{\frac{π}{2}} \frac{1 - cos ( 2 x )}{2} d x

What is the integral from 0 to ln(2) of e^x(1+e^x)^2 ?
The integral from 0 to ln(2) of e^x(1+e^x)^2 is 19/3