What is the integral of u-1/(u^2) ?

The integral of u-1/(u^2) is (u^2)/2+1/u+C

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integral of u-1/(u^2)

\int u - \frac{1}{u ^{2}} d u

\frac{u ^{2}}{2} + \frac{1}{u} + C

Solution steps

\int u - \frac{1}{u ^{2}} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u d u - \int \frac{1}{u ^{2}} d u

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

\int \frac{1}{u ^{2}} d u = - \frac{1}{u}

= \frac{u ^{2}}{2} - (- \frac{1}{u})

Simplify

= \frac{u ^{2}}{2} + \frac{1}{u}

Add a constant to the solution

= \frac{u ^{2}}{2} + \frac{1}{u} + C