Optimal. Leaf size=24 \[ \frac {2}{\log \left (e^{-\frac {5 (3-x)}{-7+x+x^3}} x\right )} \]
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Rubi [F]
time = 1.07, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {-98+68 x-2 x^2-62 x^3+16 x^4-2 x^6}{\left (49 x-14 x^2+x^3-14 x^4+2 x^5+x^7\right ) \log ^2\left (e^{-\frac {15-5 x}{-7+x+x^3}} x\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (-49+34 x-x^2-31 x^3+8 x^4-x^6\right )}{x \left (7-x-x^3\right )^2 \log ^2\left (e^{-\frac {15-5 x}{-7+x+x^3}} x\right )} \, dx\\ &=2 \int \frac {-49+34 x-x^2-31 x^3+8 x^4-x^6}{x \left (7-x-x^3\right )^2 \log ^2\left (e^{-\frac {15-5 x}{-7+x+x^3}} x\right )} \, dx\\ &=2 \int \left (-\frac {1}{x \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}-\frac {5 \left (-18+2 x+9 x^2\right )}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}+\frac {10}{\left (-7+x+x^3\right ) \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}\right ) \, dx\\ &=-\left (2 \int \frac {1}{x \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\right )-10 \int \frac {-18+2 x+9 x^2}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx+20 \int \frac {1}{\left (-7+x+x^3\right ) \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\\ &=-\left (2 \int \frac {1}{x \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\right )-10 \int \left (-\frac {18}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}+\frac {2 x}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}+\frac {9 x^2}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )}\right ) \, dx+20 \int \frac {1}{\left (-7+x+x^3\right ) \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\\ &=-\left (2 \int \frac {1}{x \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\right )-20 \int \frac {x}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx+20 \int \frac {1}{\left (-7+x+x^3\right ) \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx-90 \int \frac {x^2}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx+180 \int \frac {1}{\left (-7+x+x^3\right )^2 \log ^2\left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.06, size = 22, normalized size = 0.92 \begin {gather*} \frac {2}{\log \left (e^{\frac {5 (-3+x)}{-7+x+x^3}} x\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.19, size = 168, normalized size = 7.00
method | result | size |
risch | \(\frac {4 i}{\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i {\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right )^{2}-\pi \,\mathrm {csgn}\left (i {\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right ) \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right )^{2}+\pi \mathrm {csgn}\left (i x \,{\mathrm e}^{\frac {5 x -15}{x^{3}+x -7}}\right )^{3}+2 i \ln \left (x \right )-2 i \ln \left ({\mathrm e}^{-\frac {5 \left (x -3\right )}{x^{3}+x -7}}\right )}\) | \(168\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.35, size = 24, normalized size = 1.00 \begin {gather*} \frac {2 \, {\left (x^{3} + x - 7\right )}}{{\left (x^{3} + x - 7\right )} \log \left (x\right ) + 5 \, x - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 21, normalized size = 0.88 \begin {gather*} \frac {2}{\log \left (x e^{\left (\frac {5 \, {\left (x - 3\right )}}{x^{3} + x - 7}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.13, size = 17, normalized size = 0.71 \begin {gather*} \frac {2}{\log {\left (x e^{- \frac {15 - 5 x}{x^{3} + x - 7}} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 29, normalized size = 1.21 \begin {gather*} \frac {2 \, {\left (x^{3} + x - 7\right )}}{x^{3} \log \left (x\right ) + x \log \left (x\right ) + 5 \, x - 7 \, \log \left (x\right ) - 15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.26, size = 32, normalized size = 1.33 \begin {gather*} \frac {2\,x^3+2\,x-14}{5\,x-7\,\ln \left (x\right )+x^3\,\ln \left (x\right )+x\,\ln \left (x\right )-15} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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