What is the integral of e^xsqrt(8+e^x) ?

The integral of e^xsqrt(8+e^x) is 2/3 (8+e^x)^{3/2}+C

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integral of e^xsqrt(8+e^x)

\int e^{x} 8 + e^{x} d x

\frac{2}{3} (8 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 8 + 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 = 8 + e^{x}

= \frac{2}{3} (8 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (8 + e^{x})^{\frac{3}{2}} + C

y^{^{'}} = \frac{( e ^{(x - y)} )}{1 + e ^{x}}

\int e^{- \frac{x}{10}} d x

\frac{d}{d x} (20 - 2 x)

\frac{d}{d x} (\frac{x ^{4}}{8} ln (x) - \frac{x ^{4}}{32})

y = \frac{8}{x + 1}

What is the integral of e^xsqrt(8+e^x) ?
The integral of e^xsqrt(8+e^x) is 2/3 (8+e^x)^{3/2}+C