Solve ∫ 2/u^3du=

$$\int \frac { 2 } { u ^ { 3 } } d u =$$

Evaluate

$$-\frac{1}{u^{2}}+С$$

Solution Steps

Factor out the constant using \int af\left(u\right)\mathrm{d}u=a\int f\left(u\right)\mathrm{d}u.

$$2\int \frac{1}{u^{3}}\mathrm{d}u$$

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}}. Multiply 2 times -\frac{1}{2u^{2}}.

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

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.

$$-\frac{1}{u^{2}}+С$$

Differentiate w.r.t. u

$$\frac{2}{u^{3}}$$