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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

tangent of f(x)=4x^3-4x,(-1,0)tangent of

f (x) = 4 x^{3} - 4 x, (- 1, 0)

tangent of f(x)=2e^{2x^2+3x},\at x=0 tangent of

f (x) = 2 e^{2 x^{2} + 3 x}, at x = 0

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

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

(\partial)/(\partial x)(sin(5pix+4y))

\frac{\partial}{\partial x} (sin (5 π x + 4 y))

derivative of (1/(e^x)^{100})

\frac{d}{d x} ((\frac{1}{e ^{x}})^{100})

Frequently Asked Questions (FAQ)

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