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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

Popular Examples

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

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

y^{''}-2y^'+y=0

y^{^{''}} - 2 y^{^{'}} + y = 0

integral of x(12x+4)

\int x (12 x + 4) d x

limit as x approaches 2 of ln|2-x|

x \to 2 lim (ln ∣ 2 - x ∣)

tangent of f(x)=-x^3+9x^2-6x+9,\at x=7 tangent of

f (x) = - x^{3} + 9 x^{2} - 6 x + 9, at x = 7

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