Optimal. Leaf size=19 \[ x^2-\left (19-e^x+\log ^2(x)\right )^2 \]
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Rubi [B] time = 0.10, antiderivative size = 41, normalized size of antiderivative = 2.16, number of steps used = 9, number of rules used = 6, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {14, 2194, 2288, 2301, 2302, 30} \begin {gather*} x^2-e^{2 x}-\log ^4(x)-38 \log ^2(x)+\frac {2 e^x \left (19 x+x \log ^2(x)\right )}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rule 30
Rule 2194
Rule 2288
Rule 2301
Rule 2302
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-2 e^{2 x}+\frac {2 e^x \left (19 x+2 \log (x)+x \log ^2(x)\right )}{x}+\frac {2 \left (x^2-38 \log (x)-2 \log ^3(x)\right )}{x}\right ) \, dx\\ &=-\left (2 \int e^{2 x} \, dx\right )+2 \int \frac {e^x \left (19 x+2 \log (x)+x \log ^2(x)\right )}{x} \, dx+2 \int \frac {x^2-38 \log (x)-2 \log ^3(x)}{x} \, dx\\ &=-e^{2 x}+\frac {2 e^x \left (19 x+x \log ^2(x)\right )}{x}+2 \int \left (x-\frac {38 \log (x)}{x}-\frac {2 \log ^3(x)}{x}\right ) \, dx\\ &=-e^{2 x}+x^2+\frac {2 e^x \left (19 x+x \log ^2(x)\right )}{x}-4 \int \frac {\log ^3(x)}{x} \, dx-76 \int \frac {\log (x)}{x} \, dx\\ &=-e^{2 x}+x^2-38 \log ^2(x)+\frac {2 e^x \left (19 x+x \log ^2(x)\right )}{x}-4 \operatorname {Subst}\left (\int x^3 \, dx,x,\log (x)\right )\\ &=-e^{2 x}+x^2-38 \log ^2(x)-\log ^4(x)+\frac {2 e^x \left (19 x+x \log ^2(x)\right )}{x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 34, normalized size = 1.79 \begin {gather*} -361+38 e^x-e^{2 x}+x^2+2 \left (-19+e^x\right ) \log ^2(x)-\log ^4(x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 30, normalized size = 1.58 \begin {gather*} -\log \relax (x)^{4} + 2 \, {\left (e^{x} - 19\right )} \log \relax (x)^{2} + x^{2} - e^{\left (2 \, x\right )} + 38 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 34, normalized size = 1.79 \begin {gather*} -\log \relax (x)^{4} + 2 \, e^{x} \log \relax (x)^{2} + x^{2} - 38 \, \log \relax (x)^{2} - e^{\left (2 \, x\right )} + 38 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 32, normalized size = 1.68
method | result | size |
risch | \(-\ln \relax (x )^{4}+\left (2 \,{\mathrm e}^{x}-38\right ) \ln \relax (x )^{2}+x^{2}-{\mathrm e}^{2 x}+38 \,{\mathrm e}^{x}\) | \(32\) |
default | \(2 \,{\mathrm e}^{x} \ln \relax (x )^{2}+38 \,{\mathrm e}^{x}+x^{2}-{\mathrm e}^{2 x}-\ln \relax (x )^{4}-38 \ln \relax (x )^{2}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.41, size = 34, normalized size = 1.79 \begin {gather*} -\log \relax (x)^{4} + 2 \, e^{x} \log \relax (x)^{2} + x^{2} - 38 \, \log \relax (x)^{2} - e^{\left (2 \, x\right )} + 38 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.67, size = 34, normalized size = 1.79 \begin {gather*} 38\,{\mathrm {e}}^x-{\mathrm {e}}^{2\,x}-38\,{\ln \relax (x)}^2-{\ln \relax (x)}^4+2\,{\mathrm {e}}^x\,{\ln \relax (x)}^2+x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.39, size = 31, normalized size = 1.63 \begin {gather*} x^{2} + \left (2 \log {\relax (x )}^{2} + 38\right ) e^{x} - e^{2 x} - \log {\relax (x )}^{4} - 38 \log {\relax (x )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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