What is the integral of xpi^x ?

The integral of xpi^x is (pi^xx)/(ln(pi))-1/(ln^2(pi))pi^x+C

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integral of xpi^x

\int x π^{x} d x

\frac{π ^{x} x}{ln ( π )} - \frac{1}{ln ^{2} ( π )} π^{x} + C

Solution steps

\int x π^{x} d x

Apply Integration By Parts

: \frac{π ^{x} x}{ln ( π )} - \int \frac{π ^{x}}{ln ( π )} d x

= \frac{π ^{x} x}{ln ( π )} - \int \frac{π ^{x}}{ln ( π )} d x

\int \frac{π ^{x}}{ln ( π )} d x = \frac{1}{ln ^{2} ( π )} π^{x}

= \frac{π ^{x} x}{ln ( π )} - \frac{1}{ln ^{2} ( π )} π^{x}

Add a constant to the solution

= \frac{π ^{x} x}{ln ( π )} - \frac{1}{ln ^{2} ( π )} π^{x} + C

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What is the integral of xpi^x ?
The integral of xpi^x is (pi^xx)/(ln(pi))-1/(ln^2(pi))pi^x+C