Solve ∫ 1/3y wrt y=

$$\int \frac { 1 } { 3 y } d y =$$

Evaluate

$$\frac{\ln(|y|)}{3}+С$$

Solution Steps

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

$$\frac{\int \frac{1}{y}\mathrm{d}y}{3}$$

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

$$\frac{\ln(|y|)}{3}$$

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

$$\frac{\ln(|y|)}{3}+С$$

Differentiate w.r.t. y

$$\frac{1}{3y}$$