Optimal. Leaf size=18 \[ \frac {400}{9 e^{10} x^2 (-x+\log (4))} \]
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Rubi [A] time = 0.03, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 4, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {1594, 27, 12, 74} \begin {gather*} -\frac {400}{9 e^{10} x^2 (x-\log (4))} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 27
Rule 74
Rule 1594
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1200 x-800 \log (4)}{x^3 \left (9 e^{10} x^2-18 e^{10} x \log (4)+9 e^{10} \log ^2(4)\right )} \, dx\\ &=\int \frac {1200 x-800 \log (4)}{9 e^{10} x^3 (x-\log (4))^2} \, dx\\ &=\frac {\int \frac {1200 x-800 \log (4)}{x^3 (x-\log (4))^2} \, dx}{9 e^{10}}\\ &=-\frac {400}{9 e^{10} x^2 (x-\log (4))}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 18, normalized size = 1.00 \begin {gather*} -\frac {400}{9 e^{10} x^2 (x-\log (4))} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.46, size = 20, normalized size = 1.11 \begin {gather*} -\frac {400}{9 \, {\left (x^{3} e^{10} - 2 \, x^{2} e^{10} \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.45, size = 34, normalized size = 1.89 \begin {gather*} -\frac {100 \, e^{\left (-10\right )}}{9 \, {\left (x - 2 \, \log \relax (2)\right )} \log \relax (2)^{2}} + \frac {100 \, {\left (x + 2 \, \log \relax (2)\right )} e^{\left (-10\right )}}{9 \, x^{2} \log \relax (2)^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 18, normalized size = 1.00
method | result | size |
risch | \(\frac {400 \,{\mathrm e}^{-10}}{9 \left (2 \ln \relax (2)-x \right ) x^{2}}\) | \(18\) |
gosper | \(\frac {400 \,{\mathrm e}^{-10}}{9 \left (2 \ln \relax (2)-x \right ) x^{2}}\) | \(20\) |
norman | \(\frac {400 \,{\mathrm e}^{-10}}{9 \left (2 \ln \relax (2)-x \right ) x^{2}}\) | \(20\) |
default | \(\frac {400 \,{\mathrm e}^{-10} \left (\frac {1}{4 \ln \relax (2)^{2} x}+\frac {1}{2 \ln \relax (2) x^{2}}-\frac {1}{4 \ln \relax (2)^{2} \left (x -2 \ln \relax (2)\right )}\right )}{9}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 20, normalized size = 1.11 \begin {gather*} -\frac {400}{9 \, {\left (x^{3} e^{10} - 2 \, x^{2} e^{10} \log \relax (2)\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.86, size = 19, normalized size = 1.06 \begin {gather*} \frac {400\,{\mathrm {e}}^{-10}}{9\,\left (2\,x^2\,\ln \relax (2)-x^3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.20, size = 22, normalized size = 1.22 \begin {gather*} - \frac {400}{9 x^{3} e^{10} - 18 x^{2} e^{10} \log {\relax (2 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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