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

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

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integral of (e^{5x}-5/x)

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

\frac{1}{5} e^{5 x} - 5 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{1}{5} e^{5 x} - 5 ln ∣ x ∣

Add a constant to the solution

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

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