What is the integral of (pi+3)/(e^{3x)} ?

The integral of (pi+3)/(e^{3x)} is -(pi+3)/3 e^{-3x}+C

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integral of (pi+3)/(e^{3x)}

\int \frac{π + 3}{e ^{3 x}} d x

- \frac{π + 3}{3} e^{- 3 x} + C

Solution steps

\int \frac{π + 3}{e ^{3 x}} d x

Take the constant out:

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

= (π + 3) \cdot \int \frac{1}{e ^{3 x}} d x

\int \frac{1}{e ^{3 x}} d x = - \frac{1}{3} e^{- 3 x}

= (π + 3) (- \frac{1}{3} e^{- 3 x})

Simplify

(π + 3) (- \frac{1}{3} e^{- 3 x}) : - \frac{π + 3}{3} e^{- 3 x}

= - \frac{π + 3}{3} e^{- 3 x}

Add a constant to the solution

= - \frac{π + 3}{3} e^{- 3 x} + C

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What is the integral of (pi+3)/(e^{3x)} ?
The integral of (pi+3)/(e^{3x)} is -(pi+3)/3 e^{-3x}+C