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Popular >

integral of 2-2/x

Solution

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

Solution

2 x - 2 ln ∣ x ∣ + C

Solution steps

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

\int 2 d x = 2 x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= 2 x - 2 ln ∣ x ∣

Add a constant to the solution

= 2 x - 2 ln ∣ x ∣ + C

Popular Examples

integral of (2x-10)/(x^2-10x+106)

\int \frac{2 x - 10}{x ^{2} - 10 x + 106} d x

integral of (-5x^3)/(x^3+1)

\int \frac{- 5 x ^{3}}{x ^{3} + 1} d x

integral of (4x^3+x+1)/((x-1)(x^2+x+1))

\int \frac{4 x ^{3} + x + 1}{( x - 1 ) ( x ^{2} + x + 1 )} d x

integral of rcsin(x)

\int d arcsin (x) d x

integral of 7sin^7(x)

\int 7 sin^{7} (x) d x

Frequently Asked Questions (FAQ)

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