What is the integral of (8-3xe^x)/x ?

The integral of (8-3xe^x)/x is 8ln|x|-3e^x+C

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integral of (8-3xe^x)/x

\int \frac{8 - 3 x e ^{x}}{x} d x

8 ln ∣ x ∣ - 3 e^{x} + C

Solution steps

\int \frac{8 - 3 x e ^{x}}{x} d x

Expand

\frac{8 - 3 x e ^{x}}{x} : \frac{8}{x} - 3 e^{x}

= \int \frac{8}{x} - 3 e^{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{8}{x} d x - \int 3 e^{x} d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

\int 3 e^{x} d x = 3 e^{x}

= 8 ln ∣ x ∣ - 3 e^{x}

Add a constant to the solution

= 8 ln ∣ x ∣ - 3 e^{x} + C

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What is the integral of (8-3xe^x)/x ?
The integral of (8-3xe^x)/x is 8ln|x|-3e^x+C