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Popular Calculus >

integral of 5/x-9e^x

Solution

\int \frac{5}{x} - 9 e^{x} d x

Solution

5 ln ∣ x ∣ - 9 e^{x} + C

Solution steps

\int \frac{5}{x} - 9 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{5}{x} d x - \int 9 e^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 9 e^{x} d x = 9 e^{x}

= 5 ln ∣ x ∣ - 9 e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ - 9 e^{x} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 5/x-9e^x ?
The integral of 5/x-9e^x is 5ln|x|-9e^x+C