What is the integral of pi^x+pi^pi+x^pi ?

The integral of pi^x+pi^pi+x^pi is (pi^x)/(ln(pi))+pi^pix+(x^{pi+1})/(pi+1)+C

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integral of pi^x+pi^pi+x^pi

\int π^{x} + π^{π} + x^{π} d x

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

Solution steps

\int π^{x} + π^{π} + x^{π} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int π^{x} d x + \int π^{π} d x + \int x^{π} d x

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

\int π^{π} d x = π^{π} x

\int x^{π} d x = \frac{x ^{π + 1}}{π + 1}

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

Add a constant to the solution

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

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What is the integral of pi^x+pi^pi+x^pi ?
The integral of pi^x+pi^pi+x^pi is (pi^x)/(ln(pi))+pi^pix+(x^{pi+1})/(pi+1)+C