Solve ∫ (lny)^2

$$\int ( \ln y ) ^ { 2 }$$

Evaluate

$$x\ln(y)^{2}+С$$

Solution Steps

Find the integral of \left(\log_{e}\left(y\right)\right)^{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\left(\log_{e}\left(y\right)\right)^{2}x$$

Simplify.

$$\ln(y)^{2}x$$

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

$$\ln(y)^{2}x+С$$

Differentiate w.r.t. x

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