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Popular >

integral of 5/x-6e^x

Solution

\int \frac{5}{x} - 6 e^{x} d x

Solution

5 ln ∣ x ∣ - 6 e^{x} + C

Solution steps

\int \frac{5}{x} - 6 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 6 e^{x} d x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

\int 6 e^{x} d x = 6 e^{x}

= 5 ln ∣ x ∣ - 6 e^{x}

Add a constant to the solution

= 5 ln ∣ x ∣ - 6 e^{x} + C

Popular Examples

integral of-y^{-1}

\int - y^{- 1} d y

integral of (x^5-7)/(x^2)

\int \frac{x ^{5} - 7}{x ^{2}} d x

integral of 1^{-x^2}

\int 1 d e^{- x^{2}}

integral of sqrt(x)^2

\int x^{2} d x

integral of (x^5+3)/(x^3-4x)

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

Frequently Asked Questions (FAQ)

What is the integral of 5/x-6e^x ?
The integral of 5/x-6e^x is 5ln|x|-6e^x+C