Solve ∫ ln^2(x) wrt x

$$\int \ln ^ { 2 } ( x ) d x$$

Evaluate

$$x\ln(x^{2})-2x+С$$

Solution Steps

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

$$\frac{\ln(x^{2})x-2x}{\ln(e)}$$

Simplify.

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

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.

$$\ln(x^{2})x-2x+С$$

Differentiate w.r.t. x

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