Solve ∫ -3lny*y wrt y

$$\int - 3 \ln y * y d y$$

Evaluate

$$-3y\ln(y^{2})+6y+С$$

Solution Steps

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

$$\left(-\frac{3}{\ln(e)}\right)\int \ln(yy)\mathrm{d}y$$

Simplify.

$$\left(-\frac{3}{\ln(e)}\right)\left(\ln(y^{2})y-2y\right)$$

Simplify.

$$-3\ln(y^{2})y+6y$$

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.

$$-3\ln(y^{2})y+6y+С$$

Differentiate w.r.t. y

$$-3\ln(y^{2})$$