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Popular >

integral of 2/x-3e^x

Solution

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

Solution

2 ln ∣ x ∣ - 3 e^{x} + C

Solution steps

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ - 3 e^{x}

Add a constant to the solution

= 2 ln ∣ x ∣ - 3 e^{x} + C

Graph

Popular Examples

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\int b sin (x) cos (x) d x

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\int (x^{2} - 3 x) e^{\frac{- x}{3}} d x

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\int \frac{1}{3 y - 1} d y

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\int (tan^{2} (3 x)) + 10 d x

integral of (sin(4t-1))/(1-sin^2(4t-1))

\int \frac{sin ( 4 t - 1 )}{1 - sin ^{2} ( 4 t - 1 )} d t

Frequently Asked Questions (FAQ)

What is the integral of 2/x-3e^x ?
The integral of 2/x-3e^x is 2ln|x|-3e^x+C