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Popular >

integral of ((1-x)/x)

Solution

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

Solution

ln ∣ x ∣ - x + C

Solution steps

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

Expand

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

= \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

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\int cot (28 x) d x

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\int 4 4 - y^{2} d y

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\int 10 e^{3 x} + 1 d x

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\int sin^{3} (x) \cdot cos^{5} (x) d x

integral of ((x^3)/3+1/(4x^2))

\int (\frac{x ^{3}}{3} + \frac{1}{4 x ^{2}}) d x

Frequently Asked Questions (FAQ)

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