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Popular >

integral of 4/x-5e^x

Solution

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

Solution

4 ln ∣ x ∣ - 5 e^{x} + C

Solution steps

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

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

= 4 ln ∣ x ∣ - 5 e^{x}

Add a constant to the solution

= 4 ln ∣ x ∣ - 5 e^{x} + C

Popular Examples

integral of e^{3x^3}x^2

\int e^{3 x^{3}} x^{2} d x

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

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

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

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

integral of ((e^x))/(e^x+2)

\int \frac{( e ^{x} )}{e ^{x} + 2} d x

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

\int \frac{x + 3}{x ^{2} + 2 x + 1} d x

Frequently Asked Questions (FAQ)

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