What is the integral of (6-4xe^x)/x ?

The integral of (6-4xe^x)/x is 6ln|x|-4e^x+C

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integral of (6-4xe^x)/x

\int \frac{6 - 4 x e ^{x}}{x} d x

6 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

\int \frac{6 - 4 x e ^{x}}{x} d x

Expand

\frac{6 - 4 x e ^{x}}{x} : \frac{6}{x} - 4 e^{x}

= \int \frac{6}{x} - 4 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{6}{x} d x - \int 4 e^{x} d x

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int 4 e^{x} d x = 4 e^{x}

= 6 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 6 ln ∣ x ∣ - 4 e^{x} + C

What is the integral of (6-4xe^x)/x ?
The integral of (6-4xe^x)/x is 6ln|x|-4e^x+C