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Popular Calculus >

integral of (xy-1)/x

Solution

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

Solution

- ln ∣ x ∣ + y x + C

Solution steps

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

Expand

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int y d x = y x

= - ln ∣ x ∣ + y x

Add a constant to the solution

= - ln ∣ x ∣ + y x + C

Graph

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Frequently Asked Questions (FAQ)

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