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Popular >

integral of-3/x+3e^x

Solution

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

Solution

- 3 ln ∣ x ∣ + 3 e^{x} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= - 3 ln ∣ x ∣ + 3 e^{x}

Add a constant to the solution

= - 3 ln ∣ x ∣ + 3 e^{x} + C

Popular Examples

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

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

y^{^{'}} = 5 y^{2} + x y^{2}

derivative of 1/2 ln(1+x^2)derivative of

\frac{1}{2} ln (1 + x^{2})

limit as n approaches infinity of n^{-2}e^{3n}

n \to \infty lim (n^{- 2} e^{3 n})

slope of (-2,-4),(2,2)slope

(- 2, - 4), (2, 2)

Frequently Asked Questions (FAQ)

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