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Popular >

integral of 3/x-4e^x

Solution

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

Solution

3 ln ∣ x ∣ - 4 e^{x} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 4 e^{x} d x = 4 e^{x}

= 3 ln ∣ x ∣ - 4 e^{x}

Add a constant to the solution

= 3 ln ∣ x ∣ - 4 e^{x} + C

Popular Examples

integral of x^2(7+x)^2

\int x^{2} (7 + x)^{2} d x

integral of e^{2+x}cos(e^x+1)

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

integral of ((x-2)^2)/(\sqrt[3]{x)}

integral of 12x^{3/4}-9x^{5/3}

\int 12 x^{\frac{3}{4}} - 9 x^{\frac{5}{3}} d x

integral of x^3*sqrt(x)

\int x^{3} \cdot x d x

Frequently Asked Questions (FAQ)

What is the integral of 3/x-4e^x ?
The integral of 3/x-4e^x is 3ln|x|-4e^x+C