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Popular Calculus >

integral of 8/x-5e^x

Solution

\int \frac{8}{x} - 5 e^{x} d x

Solution

8 ln ∣ x ∣ - 5 e^{x} + C

Solution steps

\int \frac{8}{x} - 5 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{8}{x} d x - \int 5 e^{x} d x

\int \frac{8}{x} d x = 8 ln ∣ x ∣

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

= 8 ln ∣ x ∣ - 5 e^{x}

Add a constant to the solution

= 8 ln ∣ x ∣ - 5 e^{x} + C

Graph

Popular Examples

integral of ((-7)/x+e^{9x}+9/4)

\int (\frac{- 7}{x} + e^{9 x} + \frac{9}{4}) d x

integral of 2xcos(x^2+1)

\int 2 x cos (x^{2} + 1) d x

integral of x(x^2+3)^8

\int x (x^{2} + 3)^{8} d x

integral of (12-8x)^3

\int (12 - 8 x)^{3} d x

integral of x^2(5+2x^3)^2

\int x^{2} (5 + 2 x^{3})^{2} d x

Frequently Asked Questions (FAQ)

What is the integral of 8/x-5e^x ?
The integral of 8/x-5e^x is 8ln|x|-5e^x+C