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Popular >

integral of 5e^x+4/x

Solution

\int 5 e^{x} + \frac{4}{x} d x

Solution

5 e^{x} + 4 ln ∣ x ∣ + C

Solution steps

\int 5 e^{x} + \frac{4}{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{4}{x} d x

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= 5 e^{x} + 4 ln ∣ x ∣

Add a constant to the solution

= 5 e^{x} + 4 ln ∣ x ∣ + C

Popular Examples

integral of (e^{9x})

\int (e^{9 x}) d x

integral of x^{3/4}-1/(x^{3/4)}

\int x^{\frac{3}{4}} - \frac{1}{x ^{\frac{3}{4}}} d x

integral of (x^3+2x+1)

\int (x^{3} + 2 x + 1) d x

integral of 7x^{1/2}

\int 7 x^{\frac{1}{2}} d x

integral of (1/(7x-2)-1/(7x+2))

\int (\frac{1}{7 x - 2} - \frac{1}{7 x + 2}) d x

Frequently Asked Questions (FAQ)

What is the integral of 5e^x+4/x ?
The integral of 5e^x+4/x is 5e^x+4ln|x|+C