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Popular Calculus >

integral of x-2/x

Solution

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

Solution

\frac{x ^{2}}{2} - 2 ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= \frac{x ^{2}}{2} - 2 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{2}}{2} - 2 ln ∣ x ∣ + C

Graph

Popular Examples

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\frac{\partial}{\partial x} (5 x^{2})

integral of x/(sqrt(6-x^2))

\int \frac{x}{6 - x ^{2}} d x

(\partial)/(\partial x)(ye^{x^2})

\frac{\partial}{\partial x} (y e^{x^{2}})

integral of (x+4)/(x^2+5x-6)

\int \frac{x + 4}{x ^{2} + 5 x - 6} d x

(dy)/(dx)=6sqrt(xy)

\frac{d y}{d x} = 6 x y

Frequently Asked Questions (FAQ)

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