Solve ∫ 2/udu

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

Evaluate

$$2\ln(|u|)+С$$

Solution Steps

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

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

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

$$2\ln(|u|)$$

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.

$$2\ln(|u|)+С$$

Differentiate w.r.t. u

$$\frac{2}{u}$$