Solve ∫ (from 1 to e) of ln^2x wrt x=

$$\int _ { 1 } ^ { e } \ln ^ { 2 } x d x =$$

Evaluate

$$2$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \log_{e}\left(x^{2}\right)\mathrm{d}x$$

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.

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

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$\ln(e^{2})e-2e-\left(\ln(1^{2})\times 1-2\right)$$

Simplify.

$$2$$