Solve ∫ du/u^2u=

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

Evaluate

$$-\frac{1}{2u^{2}}+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\int \frac{1}{u^{3}}\mathrm{d}u$$

Since \int u^{k}\mathrm{d}u=\frac{u^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{u^{3}}\mathrm{d}u with -\frac{1}{2u^{2}}.

$$-\frac{1}{2u^{2}}$$

If F\left(u\right) is an antiderivative of f\left(u\right), then the set of all antiderivatives of f\left(u\right) is given by F\left(u\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-\frac{1}{2u^{2}}+С$$

Differentiate w.r.t. u

$$\frac{1}{u^{3}}$$