What is the integral of e^xsqrt(e^x+5) ?

The integral of e^xsqrt(e^x+5) is 2/3 (e^x+5)^{3/2}+C

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integral of e^xsqrt(e^x+5)

\int e^{x} e^{x} + 5 d x

\frac{2}{3} (e^{x} + 5)^{\frac{3}{2}} + C

Solution steps

\int e^{x} e^{x} + 5 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 = e^{x} + 5

= \frac{2}{3} (e^{x} + 5)^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (e^{x} + 5)^{\frac{3}{2}} + C

\frac{d y}{d x} = (x + y)^{2}

f (x) = \frac{1}{2 x}, at x = 9

f (x) = (x^{4} - \frac{5}{x ^{3}})^{- 4}

\int_{0}^{3} \frac{x}{x + 1} d x

n = 1 \sum \infty \frac{2 n}{3 n - 2}

What is the integral of e^xsqrt(e^x+5) ?
The integral of e^xsqrt(e^x+5) is 2/3 (e^x+5)^{3/2}+C