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

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

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

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

5 e^{x} - ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= 5 e^{x} - ln ∣ x ∣

Add a constant to the solution

= 5 e^{x} - ln ∣ x ∣ + C

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