What is the integral of (5e^x-1/(3x)-4) ?

The integral of (5e^x-1/(3x)-4) is 5e^x-1/3 ln|x|-4x+C

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integral of (5e^x-1/(3x)-4)

\int (5 e^{x} - \frac{1}{3 x} - 4) d x

5 e^{x} - \frac{1}{3} ln ∣ x ∣ - 4 x + C

Solution steps

\int 5 e^{x} - \frac{1}{3 x} - 4 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 5 e^{x} d x - \int \frac{1}{3 x} d x - \int 4 d x

\int 5 e^{x} d x = 5 e^{x}

\int \frac{1}{3 x} d x = \frac{1}{3} ln ∣ x ∣

\int 4 d x = 4 x

= 5 e^{x} - \frac{1}{3} ln ∣ x ∣ - 4 x

Add a constant to the solution

= 5 e^{x} - \frac{1}{3} ln ∣ x ∣ - 4 x + C

What is the integral of (5e^x-1/(3x)-4) ?
The integral of (5e^x-1/(3x)-4) is 5e^x-1/3 ln|x|-4x+C