What is the integral of pi^{3t} ?

The integral of pi^{3t} is (pi^{3t})/(3ln(pi))+C

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integral of pi^{3t}

\int π^{3 t} d t

\frac{π ^{3 t}}{3 ln ( π )} + C

Solution steps

\int π^{3 t} d t

Apply u-substitution

: \int π^{u} \frac{1}{3} d u

= \int π^{u} \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int π^{u} d u

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

= \frac{1}{3} \cdot \frac{π ^{u}}{ln ( π )}

Substitute back

u = 3 t

= \frac{1}{3} \cdot \frac{π ^{3 t}}{ln ( π )}

Simplify

\frac{1}{3} \cdot \frac{π ^{3 t}}{ln ( π )} : \frac{π ^{3 t}}{3 ln ( π )}

= \frac{π ^{3 t}}{3 ln ( π )}

Add a constant to the solution

= \frac{π ^{3 t}}{3 ln ( π )} + C

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What is the integral of pi^{3t} ?
The integral of pi^{3t} is (pi^{3t})/(3ln(pi))+C