Evaluate
8\left(\ln(2)-1\right)\approx -2.454822556
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\int \log_{e}\left(x^{2}\right)\mathrm{d}x
Evaluate the indefinite integral first.
\frac{\ln(x^{2})x-2x}{\ln(e)}
Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.
\ln(x^{2})x-2x
Simplify.
\ln(2^{2})\times 2-2\times 2-\left(\ln(\left(-2\right)^{2})\left(-2\right)-2\left(-2\right)\right)
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.
8\ln(2)-8
Simplify.
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Simultaneous equation
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Integration
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Limits
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