Optimal. Leaf size=24 \[ \frac {x}{\frac {19}{4}+\left (9 (6+x)^2+\log (2-x)\right )^2} \]
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Rubi [F]
time = 5.92, 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 {-3359384+1669324 x+556416 x^2-155808 x^3-54432 x^4-3888 x^5+\left (-20736+10336 x+576 x^2-288 x^3\right ) \log (2-x)+(-32+16 x) \log ^2(2-x)}{-352670651858-293870933783 x-39176763264 x^2+45714497472 x^3+26665854480 x^4+6983855640 x^5+1058158080 x^6+95738112 x^7+4828896 x^8+104976 x^9+\left (-4353761664-2176749504 x+362824416 x^2+503887536 x^3+151165440 x^4+21835008 x^5+1586304 x^6+46656 x^7\right ) \log (2-x)+\left (-20155696-3359080 x+3359232 x^2+1306368 x^3+171072 x^4+7776 x^5\right ) \log ^2(2-x)+\left (-41472+6912 x+5760 x^2+576 x^3\right ) \log ^3(2-x)+(-32+16 x) \log ^4(2-x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (839846-417331 x-139104 x^2+38952 x^3+13608 x^4+972 x^5+8 \left (648-323 x-18 x^2+9 x^3\right ) \log (2-x)-4 (-2+x) \log ^2(2-x)\right )}{(2-x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \frac {839846-417331 x-139104 x^2+38952 x^3+13608 x^4+972 x^5+8 \left (648-323 x-18 x^2+9 x^3\right ) \log (2-x)-4 (-2+x) \log ^2(2-x)}{(2-x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \left (-\frac {8 x \left (-215+72 x+18 x^2\right ) \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)}\right ) \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \frac {x \left (-215+72 x+18 x^2\right ) \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \left (\frac {324+108 x+9 x^2+\log (2-x)}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {2 \left (324+108 x+9 x^2+\log (2-x)\right )}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {108 x \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}+\frac {18 x^2 \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2}\right ) \, dx\\ &=4 \int \frac {1}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)} \, dx-32 \int \frac {324+108 x+9 x^2+\log (2-x)}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-64 \int \frac {324+108 x+9 x^2+\log (2-x)}{(-2+x) \left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-576 \int \frac {x^2 \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx-3456 \int \frac {x \left (324+108 x+9 x^2+\log (2-x)\right )}{\left (419923+279936 x+69984 x^2+7776 x^3+324 x^4+2592 \log (2-x)+864 x \log (2-x)+72 x^2 \log (2-x)+4 \log ^2(2-x)\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 48, normalized size = 2.00 \begin {gather*} \frac {4 x}{419923+279936 x+69984 x^2+7776 x^3+324 x^4+72 (6+x)^2 \log (2-x)+4 \log ^2(2-x)} \end {gather*}
Antiderivative was successfully verified.
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Maple [B] Leaf count of result is larger than twice the leaf count of optimal. \(83\) vs.
\(2(25)=50\).
time = 0.38, size = 84, normalized size = 3.50
method | result | size |
risch | \(\frac {4 x}{324 x^{4}+72 \ln \left (2-x \right ) x^{2}+7776 x^{3}+4 \ln \left (2-x \right )^{2}+864 x \ln \left (2-x \right )+69984 x^{2}+2592 \ln \left (2-x \right )+279936 x +419923}\) | \(64\) |
derivativedivides | \(\frac {4 x}{324 \left (2-x \right )^{4}-10368 \left (2-x \right )^{3}+72 \ln \left (2-x \right ) \left (2-x \right )^{2}+124416 \left (2-x \right )^{2}-1152 \left (2-x \right ) \ln \left (2-x \right )+4 \ln \left (2-x \right )^{2}+19+663552 x +4608 \ln \left (2-x \right )}\) | \(84\) |
default | \(\frac {4 x}{324 \left (2-x \right )^{4}-10368 \left (2-x \right )^{3}+72 \ln \left (2-x \right ) \left (2-x \right )^{2}+124416 \left (2-x \right )^{2}-1152 \left (2-x \right ) \ln \left (2-x \right )+4 \ln \left (2-x \right )^{2}+19+663552 x +4608 \ln \left (2-x \right )}\) | \(84\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (25) = 50\).
time = 0.31, size = 51, normalized size = 2.12 \begin {gather*} \frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 51 vs.
\(2 (25) = 50\).
time = 0.37, size = 51, normalized size = 2.12 \begin {gather*} \frac {4 \, x}{324 \, x^{4} + 7776 \, x^{3} + 69984 \, x^{2} + 72 \, {\left (x^{2} + 12 \, x + 36\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 279936 \, x + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 46 vs.
\(2 (17) = 34\).
time = 0.14, size = 46, normalized size = 1.92 \begin {gather*} \frac {4 x}{324 x^{4} + 7776 x^{3} + 69984 x^{2} + 279936 x + \left (72 x^{2} + 864 x + 2592\right ) \log {\left (2 - x \right )} + 4 \log {\left (2 - x \right )}^{2} + 419923} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 73 vs.
\(2 (25) = 50\).
time = 0.47, size = 73, normalized size = 3.04 \begin {gather*} \frac {4 \, x}{324 \, {\left (x - 2\right )}^{4} + 10368 \, {\left (x - 2\right )}^{3} + 72 \, {\left (x - 2\right )}^{2} \log \left (-x + 2\right ) + 124416 \, {\left (x - 2\right )}^{2} + 1152 \, {\left (x - 2\right )} \log \left (-x + 2\right ) + 4 \, \log \left (-x + 2\right )^{2} + 663552 \, x + 4608 \, \log \left (-x + 2\right ) + 19} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {1669324\,x+{\ln \left (2-x\right )}^2\,\left (16\,x-32\right )+\ln \left (2-x\right )\,\left (-288\,x^3+576\,x^2+10336\,x-20736\right )+556416\,x^2-155808\,x^3-54432\,x^4-3888\,x^5-3359384}{{\ln \left (2-x\right )}^3\,\left (576\,x^3+5760\,x^2+6912\,x-41472\right )-293870933783\,x+\ln \left (2-x\right )\,\left (46656\,x^7+1586304\,x^6+21835008\,x^5+151165440\,x^4+503887536\,x^3+362824416\,x^2-2176749504\,x-4353761664\right )+{\ln \left (2-x\right )}^2\,\left (7776\,x^5+171072\,x^4+1306368\,x^3+3359232\,x^2-3359080\,x-20155696\right )+{\ln \left (2-x\right )}^4\,\left (16\,x-32\right )-39176763264\,x^2+45714497472\,x^3+26665854480\,x^4+6983855640\,x^5+1058158080\,x^6+95738112\,x^7+4828896\,x^8+104976\,x^9-352670651858} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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