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Popular >

integral of ((x-1))/x

Solution

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

Solution

x - ln ∣ x ∣ + C

Solution steps

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

Expand

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

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

\int 1 d x = x

\int \frac{1}{x} d x = ln ∣ x ∣

= x - ln ∣ x ∣

Add a constant to the solution

= x - ln ∣ x ∣ + C

Popular Examples

integral of (x^2-x+2)

\int (x^{2} - x + 2) d x

integral of sqrt(e^{-2t)+e^{2t}+2}

\int e^{- 2 t} + e^{2 t} + 2 d t

domain of f(x)=(3x^2)^{2x}(x^2+2x)^2 domain

f (x) = (3 x^{2})^{2 x} (x^{2} + 2 x)^{2}

y^{''}-6y^'+2y=0,y(0)=0,y^'(0)=9

y^{^{''}} - 6 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 9

(dy)/(dt)= 1/5 t

\frac{d y}{d t} = \frac{1}{5} t

Frequently Asked Questions (FAQ)

What is the integral of ((x-1))/x ?
The integral of ((x-1))/x is x-ln|x|+C