Solve ∫ du/uv^4

$$\int \frac { d u } { u v ^ { 4 } }$$

Evaluate

$$\frac{\ln(|u|)}{v^{4}}+С$$

Solution Steps

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

$$\frac{\int \frac{1}{u}\mathrm{d}u}{v^{4}}$$

Use \int \frac{1}{u}\mathrm{d}u=\ln(|u|) from the table of common integrals to obtain the result.

$$\frac{\ln(|u|)}{v^{4}}$$

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.

$$\frac{\ln(|u|)}{v^{4}}+С$$

Differentiate w.r.t. u

$$\frac{1}{uv^{4}}$$