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

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

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

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

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

Decimal

2.89431 \dots

Solution steps

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

Apply u-substitution

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

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

Apply the Power Rule

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

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

Compute the boundaries:

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

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

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