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Popular >

integral of (-x+2)/x

Solution

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

Solution

- x + 2 ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{2}{x} d x = 2 ln ∣ x ∣

= - x + 2 ln ∣ x ∣

Add a constant to the solution

= - x + 2 ln ∣ x ∣ + C

Graph

Popular Examples

integral of x^2sqrt(1+y^4)

\int x^{2} 1 + y^{4} d x

integral of e^x(e^x+1)^3

\int e^{x} (e^{x} + 1)^{3} d x

integral of tan(5x)sec(5x)

\int tan (5 x) sec (5 x) d x

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

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

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

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

Frequently Asked Questions (FAQ)

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