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Popular >

integral of (3x-2/x)

Solution

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

Solution

\frac{3 x ^{2}}{2} - 2 ln ∣ x ∣ + C

Solution steps

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

\int 3 x d x = \frac{3 x ^{2}}{2}

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{3 x ^{2}}{2} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{3 x ^{2}}{2} - 2 ln ∣ x ∣ + C

Popular Examples

(dy)/(dx)=sqrt(20x+y)-20

\frac{d y}{d x} = 20 x + y - 20

integral from 7 to infinity of 9/(v^2-v)

\int_{7}^{\infty} \frac{9}{v ^{2} - v} d v

(\partial)/(\partial x)(e^{(x+y)/(x-y)})

\frac{\partial}{\partial x} (e^{\frac{x + y}{x - y}})

slope of (10.2)(19.14)slope

(10.2) (19.14)

limit as x approaches 2+of (|2-x|)/(2-x)

x \to 2 + lim (\frac{∣ 2 - x ∣}{2 - x})

Frequently Asked Questions (FAQ)

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