Optimal. Leaf size=25 \[ -5-e^{2 x^2}+2 x+x^2+\log (x)-\log ^2(x) \]
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Rubi [A] time = 0.04, antiderivative size = 24, normalized size of antiderivative = 0.96, number of steps used = 8, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14, 2209, 2301} \begin {gather*} x^2-e^{2 x^2}+2 x-\log ^2(x)+\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 2209
Rule 2301
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-4 e^{2 x^2} x+\frac {1+2 x+2 x^2-2 \log (x)}{x}\right ) \, dx\\ &=-\left (4 \int e^{2 x^2} x \, dx\right )+\int \frac {1+2 x+2 x^2-2 \log (x)}{x} \, dx\\ &=-e^{2 x^2}+\int \left (\frac {1+2 x+2 x^2}{x}-\frac {2 \log (x)}{x}\right ) \, dx\\ &=-e^{2 x^2}-2 \int \frac {\log (x)}{x} \, dx+\int \frac {1+2 x+2 x^2}{x} \, dx\\ &=-e^{2 x^2}-\log ^2(x)+\int \left (2+\frac {1}{x}+2 x\right ) \, dx\\ &=-e^{2 x^2}+2 x+x^2+\log (x)-\log ^2(x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 24, normalized size = 0.96 \begin {gather*} -e^{2 x^2}+2 x+x^2+\log (x)-\log ^2(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 23, normalized size = 0.92 \begin {gather*} x^{2} - \log \relax (x)^{2} + 2 \, x - e^{\left (2 \, x^{2}\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 23, normalized size = 0.92 \begin {gather*} x^{2} - \log \relax (x)^{2} + 2 \, x - e^{\left (2 \, x^{2}\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 24, normalized size = 0.96
method | result | size |
default | \(2 x +\ln \relax (x )+x^{2}-{\mathrm e}^{2 x^{2}}-\ln \relax (x )^{2}\) | \(24\) |
norman | \(2 x +\ln \relax (x )+x^{2}-{\mathrm e}^{2 x^{2}}-\ln \relax (x )^{2}\) | \(24\) |
risch | \(2 x +\ln \relax (x )+x^{2}-{\mathrm e}^{2 x^{2}}-\ln \relax (x )^{2}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.34, size = 23, normalized size = 0.92 \begin {gather*} x^{2} - \log \relax (x)^{2} + 2 \, x - e^{\left (2 \, x^{2}\right )} + \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.98, size = 23, normalized size = 0.92 \begin {gather*} 2\,x-{\mathrm {e}}^{2\,x^2}+\ln \relax (x)-{\ln \relax (x)}^2+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 20, normalized size = 0.80 \begin {gather*} x^{2} + 2 x - e^{2 x^{2}} - \log {\relax (x )}^{2} + \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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