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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

Popular Examples

inverse oflaplace s/((s-2)^2)inverse laplace

\frac{s}{( s - 2 ) ^{2}}

integral of (e^{-bx})/(1-e^{-bx)}

\int \frac{e ^{- b x}}{1 - e ^{- b x}} d x

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

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

derivative of f(x)=y derivative of

f (x) = y

inverse oflaplace (-s)/(s^2+25s+30)+1/s inverse laplace

\frac{- s}{s ^{2} + 25 s + 30} + \frac{1}{s}

Frequently Asked Questions (FAQ)

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