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

Apply the Power Rule

= \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

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