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Popular >

integral of 3/x+2e^x

Solution

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

Solution

3 ln ∣ x ∣ + 2 e^{x} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ + 2 e^{x}

Add a constant to the solution

= 3 ln ∣ x ∣ + 2 e^{x} + C

Graph

Popular Examples

derivative of 3x-x^2

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

derivative of (4-x^2/(4+x^2))

\frac{d}{d x} (\frac{4 - x ^{2}}{4 + x ^{2}})

integral of (x+1/(x^4sqrt(x)))

\int (x + \frac{1}{x ^{4} x}) d x

integral of sec^8(x)

\int sec^{8} (x) d x

(\partial)/(\partial x)(40xy*e^{5x^2-2y})

\frac{\partial}{\partial x} (40 x y \cdot e^{5 x^{2} - 2 y})

Frequently Asked Questions (FAQ)

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