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Popular >

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

Popular Examples

integral of sec^2(θ)tan(θ)

\int sec^{2} (θ) tan (θ) d θ

integral of e^{-(x^3)^3}x^3)^3

\int e^{- (x^{3})^{3}} d (x^{3})^{3}

limit as x approaches a+of-5

x \to a + lim (- 5)

derivative of ((x^2+3)/(x^2-3))^4 derivative of

(\frac{x ^{2} + 3}{x ^{2} - 3})^{4}

integral of ((sqrt(x^2-4)))/(x^6)

\int \frac{( x ^{2} - 4 )}{x ^{6}} d x

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