Optimal. Leaf size=32 \[ 4+3 e^{-e^2}-25 x^2 \left (-\frac {3 e^4}{x}-x+\log (4)\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 36, normalized size of antiderivative = 1.12, number of steps used = 3, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {6} \begin {gather*} -25 x^4+50 x^3 \log (4)-25 x^2 \left (6 e^4+\log ^2(4)\right )+150 e^4 x \log (4) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-100 x^3+\left (150 e^4+150 x^2\right ) \log (4)+x \left (-300 e^4-50 \log ^2(4)\right )\right ) \, dx\\ &=-25 x^4-25 x^2 \left (6 e^4+\log ^2(4)\right )+\log (4) \int \left (150 e^4+150 x^2\right ) \, dx\\ &=-25 x^4+150 e^4 x \log (4)+50 x^3 \log (4)-25 x^2 \left (6 e^4+\log ^2(4)\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 44, normalized size = 1.38 \begin {gather*} -50 \left (3 e^4 x^2+\frac {x^4}{2}-3 e^4 x \log (4)-x^3 \log (4)+\frac {1}{2} x^2 \log ^2(4)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 35, normalized size = 1.09 \begin {gather*} -25 \, x^{4} - 100 \, x^{2} \log \relax (2)^{2} - 150 \, x^{2} e^{4} + 100 \, {\left (x^{3} + 3 \, x e^{4}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 35, normalized size = 1.09 \begin {gather*} -25 \, x^{4} - 100 \, x^{2} \log \relax (2)^{2} - 150 \, x^{2} e^{4} + 100 \, {\left (x^{3} + 3 \, x e^{4}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 35, normalized size = 1.09
method | result | size |
gosper | \(25 x \left (-4 x \ln \relax (2)^{2}+4 x^{2} \ln \relax (2)-x^{3}+12 \,{\mathrm e}^{4} \ln \relax (2)-6 x \,{\mathrm e}^{4}\right )\) | \(35\) |
norman | \(\left (-100 \ln \relax (2)^{2}-150 \,{\mathrm e}^{4}\right ) x^{2}-25 x^{4}+100 x^{3} \ln \relax (2)+300 x \,{\mathrm e}^{4} \ln \relax (2)\) | \(36\) |
risch | \(-100 x^{2} \ln \relax (2)^{2}+300 x \,{\mathrm e}^{4} \ln \relax (2)+100 x^{3} \ln \relax (2)-150 x^{2} {\mathrm e}^{4}-25 x^{4}\) | \(37\) |
default | \(-100 x^{2} \ln \relax (2)^{2}+2 \ln \relax (2) \left (150 x \,{\mathrm e}^{4}+50 x^{3}\right )-150 x^{2} {\mathrm e}^{4}-25 x^{4}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 35, normalized size = 1.09 \begin {gather*} -25 \, x^{4} - 100 \, x^{2} \log \relax (2)^{2} - 150 \, x^{2} e^{4} + 100 \, {\left (x^{3} + 3 \, x e^{4}\right )} \log \relax (2) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.73, size = 36, normalized size = 1.12 \begin {gather*} -25\,x^4+100\,\ln \relax (2)\,x^3+\left (-150\,{\mathrm {e}}^4-100\,{\ln \relax (2)}^2\right )\,x^2+300\,{\mathrm {e}}^4\,\ln \relax (2)\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.07, size = 39, normalized size = 1.22 \begin {gather*} - 25 x^{4} + 100 x^{3} \log {\relax (2 )} + x^{2} \left (- 150 e^{4} - 100 \log {\relax (2 )}^{2}\right ) + 300 x e^{4} \log {\relax (2 )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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