What is the integral of pi^x-x^{-1} ?

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

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integral of pi^x-x^{-1}

\int π^{x} - x^{- 1} d x

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

Solution steps

\int π^{x} - x^{- 1} 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 x^{- 1} d x

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

\int x^{- 1} d x = ln ∣ x ∣

= \frac{π ^{x}}{ln ( π )} - ln ∣ x ∣

Add a constant to the solution

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

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