What is the integral of (x')/(x^2) ?

The integral of (x')/(x^2) is (x')/x-2/x+C

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integral of (x')/(x^2)

\int \frac{x ^{'}}{x ^{2}} d x

\frac{x '}{x} - \frac{2}{x} + C

Solution steps

\int \frac{x ^{'}}{x ^{2}} d x

\frac{x ^{'}}{x ^{2}} = (x^{'}) \frac{1}{x ^{2}}

= \int x^{^{'}} \frac{1}{x ^{2}} d x

Apply Integration By Parts

: \frac{x ^{'}}{x} - \int - \frac{2}{x ^{2}} d x

= \frac{x ^{^{'}}}{x} - \int - \frac{2}{x ^{2}} d x

\int - \frac{2}{x ^{2}} d x = \frac{2}{x}

= \frac{x ^{^{'}}}{x} - \frac{2}{x}

Add a constant to the solution

= \frac{x ^{^{'}}}{x} - \frac{2}{x} + C

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