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Popular >

integral of ((2-x))/x

Solution

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

Solution

2 ln ∣ x ∣ - x + C

Solution steps

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

Expand

\frac{2 - x}{x} : \frac{2}{x} - 1

= \int \frac{2}{x} - 1 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{2}{x} d x - \int 1 d x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 1 d x = x

= 2 ln ∣ x ∣ - x

Add a constant to the solution

= 2 ln ∣ x ∣ - x + C

Graph

Popular Examples

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

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

integral of ((-1)^x)/x

\int \frac{( - 1 ) ^{x}}{x} d x

integral of (e^{2x})/(e^{2x)-4}

\int \frac{e ^{2 x}}{e ^{2 x} - 4} d x

integral of (cos(x))(sin(x))^2

\int (cos (x)) (sin (x))^{2} d x

integral of (1+2ln(x))/x

\int \frac{1 + 2 ln ( x )}{x} d x

Frequently Asked Questions (FAQ)

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