What is the integral of (-e^2)/x+sqrt(3)*3^x ?

The integral of (-e^2)/x+sqrt(3)*3^x is -e^2ln|x|+(sqrt(3)*3^x)/(ln(3))+C

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integral of (-e^2)/x+sqrt(3)*3^x

\int \frac{- e ^{2}}{x} + 3 \cdot 3^{x} d x

- e^{2} ln ∣ x ∣ + \frac{3 \cdot 3 ^{x}}{ln ( 3 )} + C

Solution steps

\int \frac{- e ^{2}}{x} + 3 \cdot 3^{x} 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 \frac{- e ^{2}}{x} d x + \int 3 \cdot 3^{x} d x

\int \frac{- e ^{2}}{x} d x = - e^{2} ln ∣ x ∣

\int 3 \cdot 3^{x} d x = \frac{3 \cdot 3 ^{x}}{ln ( 3 )}

= - e^{2} ln ∣ x ∣ + \frac{3 \cdot 3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= - e^{2} ln ∣ x ∣ + \frac{3 \cdot 3 ^{x}}{ln ( 3 )} + C

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What is the integral of (-e^2)/x+sqrt(3)*3^x ?
The integral of (-e^2)/x+sqrt(3)*3^x is -e^2ln|x|+(sqrt(3)*3^x)/(ln(3))+C