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

The integral of x/(x') is (x^2}{x'}-\frac{x^2)/2+C

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integral of x/(x')

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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What is the integral of x/(x') ?
The integral of x/(x') is (x^2}{x'}-\frac{x^2)/2+C