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

The integral from 0 to 1 of e^xsqrt(1+e^x) is (2(1+e)^{3/2}-4sqrt(2))/3

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

\int_{0}^{1} e^{x} 1 + e^{x} d x

\frac{2 ( 1 + e ) ^{\frac{3}{2}} - 4 2}{3}

Decimal

2.89431 \dots

Solution steps

\int_{0}^{1} e^{x} 1 + e^{x} d x

Apply u-substitution

: \int_{2}^{1 + e} u d u

= \int_{2}^{1 + e} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{1 + e}

= [\frac{2}{3} u^{\frac{3}{2}}]_{2}^{1 + e}

Compute the boundaries:

\frac{2 ( 1 + e ) ^{\frac{3}{2}} - 4 2}{3}

= \frac{2 ( 1 + e ) ^{\frac{3}{2}} - 4 2}{3}

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What is the integral from 0 to 1 of e^xsqrt(1+e^x) ?
The integral from 0 to 1 of e^xsqrt(1+e^x) is (2(1+e)^{3/2}-4sqrt(2))/3