What is the integral of e^xsqrt(23+e^x) ?

The integral of e^xsqrt(23+e^x) is 2/3 (23+e^x)^{3/2}+C

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integral of e^xsqrt(23+e^x)

\int e^{x} 23 + e^{x} d x

\frac{2}{3} (23 + e^{x})^{\frac{3}{2}} + C

Solution steps

\int e^{x} 23 + 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 = 23 + e^{x}

= \frac{2}{3} (23 + e^{x})^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} (23 + e^{x})^{\frac{3}{2}} + C

y = 6 tan (\frac{x}{3}) cos (7 x)

t^{3} - 3 t

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\int 100 d x

What is the integral of e^xsqrt(23+e^x) ?
The integral of e^xsqrt(23+e^x) is 2/3 (23+e^x)^{3/2}+C