Solve ∫ x/y wrt y

$$\int{ \frac{ x }{ y } }d y$$

Evaluate

$$x\ln(|y|)+С$$

Solution Steps

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

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

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

$$x\ln(|y|)$$

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.

$$x\ln(|y|)+С$$

Differentiate w.r.t. x

$$\ln(|y|)$$