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Popular Calculus >

integral of 1/x x'

Solution

\int \frac{1}{x} x^{'} d x

Solution

x' + ln ∣ x ∣ + C

Solution steps

\int \frac{1}{x} x^{'} d x

Apply Integration By Parts

= x^{^{'}} - \int - \frac{1}{x} d x

\int - \frac{1}{x} d x = - ln ∣ x ∣

= x^{^{'}} - (- ln ∣ x ∣)

Simplify

= x^{^{'}} + ln ∣ x ∣

Add a constant to the solution

= x^{^{'}} + ln ∣ x ∣ + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of 1/x x' ?
The integral of 1/x x' is x'+ln|x|+C