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Popular >

integral of (1/x-1)

Solution

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

Solution

ln ∣ x ∣ - x + C

Solution steps

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int 1 d x = x

= ln ∣ x ∣ - x

Add a constant to the solution

= ln ∣ x ∣ - x + C

Popular Examples

integral of 6x^2sin(x^3-5)

\int 6 x^{2} sin (x^{3} - 5) d x

integral of x^{-1}(2x+x^2)

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

integral of tan^2(θ)sec^3(θ)

\int tan^{2} (θ) sec^{3} (θ) d θ

integral of (tan(x)-2)

\int (tan (x) - 2) d x

integral of x21^x

\int x 2 1^{x} d x

Frequently Asked Questions (FAQ)

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