What is the integral of pi^{2x} ?

The integral of pi^{2x} is (pi^{2x})/(2ln(pi))+C

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integral of pi^{2x}

\int π^{2 x} d x

\frac{π ^{2 x}}{2 ln ( π )} + C

Solution steps

\int π^{2 x} d x

Apply u-substitution

= \int π^{u} \frac{1}{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int π^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{1}{2} \cdot \frac{π ^{u}}{ln ( π )}

Substitute back

u = 2 x

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

Simplify

\frac{1}{2} \cdot \frac{π ^{2 x}}{ln ( π )} : \frac{π ^{2 x}}{2 ln ( π )}

= \frac{π ^{2 x}}{2 ln ( π )}

Add a constant to the solution

= \frac{π ^{2 x}}{2 ln ( π )} + C

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