What is the integral of e^xsqrt(2+e^x) ?

The integral of e^xsqrt(2+e^x) is 2/3 (2+e^x)^{3/2}+C

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integral of e^xsqrt(2+e^x)

\int e^{x} 2 + e^{x} d x

\frac{2}{3} (2 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 2 + e^{x} d x

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = 2 + e^{x}

= \frac{2}{3} (2 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (2 + e^{x})^{\frac{3}{2}} + C

\int \frac{x ^{3}}{( 4 x ^{2} + 9 ) ^{\frac{3}{2}}} d x

\frac{1}{7 - 10 e ^{x}}

\frac{d}{d x} (\frac{ln ( x + 1 )}{ln ( x - 1 )})

x^{2} e^{- 3 x}

ln (e^{x} + 1)

What is the integral of e^xsqrt(2+e^x) ?
The integral of e^xsqrt(2+e^x) is 2/3 (2+e^x)^{3/2}+C