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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

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(4 + 16 e^{8} x)^{\frac{1}{2}}

Frequently Asked Questions (FAQ)

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