What is the integral from 0 to 1 of e^xsqrt(e^x+4) ?

The integral from 0 to 1 of e^xsqrt(e^x+4) is (2(e+4)^{3/2}-10sqrt(5))/3

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integral from 0 to 1 of e^xsqrt(e^x+4)

\int_{0}^{1} e^{x} e^{x} + 4 d x

\frac{2 ( e + 4 ) ^{\frac{3}{2}} - 10 5}{3}

Decimal Notation

4.15547 \dots

Solution steps

\int_{0}^{1} e^{x} e^{x} + 4 d x

Apply u-substitution

: \int_{5}^{e + 4} u d u

= \int_{5}^{e + 4} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{e + 4}

= [\frac{2}{3} u^{\frac{3}{2}}]_{5}^{e + 4}

Compute the boundaries:

\frac{2 ( e + 4 ) ^{\frac{3}{2}} - 10 5}{3}

= \frac{2 ( e + 4 ) ^{\frac{3}{2}} - 10 5}{3}

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What is the integral from 0 to 1 of e^xsqrt(e^x+4) ?
The integral from 0 to 1 of e^xsqrt(e^x+4) is (2(e+4)^{3/2}-10sqrt(5))/3