What is the integral of e^x(sqrt(pi+e^x)) ?

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

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integral of e^x(sqrt(pi+e^x))

\int e^{x} (π + e^{x}) d x

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

Solution steps

\int e^{x} π + 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 = π + e^{x}

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

Add a constant to the solution

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

\frac{d x}{d t} = 2 x + t

\frac{1}{s ^{4}}

x^{^{''}} = - k^{2} x

(2 + x) y^{^{'}} - x y = 0

e^{s}

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