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Popular >

integral of ((x-1))/x

Solution

integral

\frac{( x - 1 )}{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 e^8xcos(x)integral

e^{8} x cos (x)

integral of (5-3x)(2+x^2)integral

(5 - 3 x) (2 + x^{2})

(d^4-2d^2+1)y=cos(x)

(d^{4} - 2 d^{2} + 1) y = cos (x)

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(d^2-9)y=e^3x+e^{-3}x

(d^{2} - 9) y = e^{3} x + e^{- 3} x

Frequently Asked Questions (FAQ)

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