Optimal. Leaf size=18 \[ \frac {\left (-20+\frac {3}{x}\right )^4}{\frac {121}{25}+\log (x)} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(18)=36\).
time = 1.03, antiderivative size = 63, normalized size of antiderivative = 3.50, number of steps
used = 30, number of rules used = 9, integrand size = 63, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {6820, 12,
6874, 2395, 2343, 2346, 2209, 2339, 30} \begin {gather*} \frac {2025}{x^4 (25 \log (x)+121)}-\frac {54000}{x^3 (25 \log (x)+121)}+\frac {540000}{x^2 (25 \log (x)+121)}-\frac {2400000}{x (25 \log (x)+121)}+\frac {4000000}{25 \log (x)+121} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rule 2209
Rule 2339
Rule 2343
Rule 2346
Rule 2395
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {25 (3-20 x)^3 (-1527+500 x-300 \log (x))}{x^5 (121+25 \log (x))^2} \, dx\\ &=25 \int \frac {(3-20 x)^3 (-1527+500 x-300 \log (x))}{x^5 (121+25 \log (x))^2} \, dx\\ &=25 \int \left (-\frac {25 (-3+20 x)^4}{x^5 (121+25 \log (x))^2}+\frac {12 (-3+20 x)^3}{x^5 (121+25 \log (x))}\right ) \, dx\\ &=300 \int \frac {(-3+20 x)^3}{x^5 (121+25 \log (x))} \, dx-625 \int \frac {(-3+20 x)^4}{x^5 (121+25 \log (x))^2} \, dx\\ &=300 \int \left (-\frac {27}{x^5 (121+25 \log (x))}+\frac {540}{x^4 (121+25 \log (x))}-\frac {3600}{x^3 (121+25 \log (x))}+\frac {8000}{x^2 (121+25 \log (x))}\right ) \, dx-625 \int \left (\frac {81}{x^5 (121+25 \log (x))^2}-\frac {2160}{x^4 (121+25 \log (x))^2}+\frac {21600}{x^3 (121+25 \log (x))^2}-\frac {96000}{x^2 (121+25 \log (x))^2}+\frac {160000}{x (121+25 \log (x))^2}\right ) \, dx\\ &=-\left (8100 \int \frac {1}{x^5 (121+25 \log (x))} \, dx\right )-50625 \int \frac {1}{x^5 (121+25 \log (x))^2} \, dx+162000 \int \frac {1}{x^4 (121+25 \log (x))} \, dx-1080000 \int \frac {1}{x^3 (121+25 \log (x))} \, dx+1350000 \int \frac {1}{x^4 (121+25 \log (x))^2} \, dx+2400000 \int \frac {1}{x^2 (121+25 \log (x))} \, dx-13500000 \int \frac {1}{x^3 (121+25 \log (x))^2} \, dx+60000000 \int \frac {1}{x^2 (121+25 \log (x))^2} \, dx-100000000 \int \frac {1}{x (121+25 \log (x))^2} \, dx\\ &=\frac {2025}{x^4 (121+25 \log (x))}-\frac {54000}{x^3 (121+25 \log (x))}+\frac {540000}{x^2 (121+25 \log (x))}-\frac {2400000}{x (121+25 \log (x))}+8100 \int \frac {1}{x^5 (121+25 \log (x))} \, dx-8100 \text {Subst}\left (\int \frac {e^{-4 x}}{121+25 x} \, dx,x,\log (x)\right )-162000 \int \frac {1}{x^4 (121+25 \log (x))} \, dx+162000 \text {Subst}\left (\int \frac {e^{-3 x}}{121+25 x} \, dx,x,\log (x)\right )+1080000 \int \frac {1}{x^3 (121+25 \log (x))} \, dx-1080000 \text {Subst}\left (\int \frac {e^{-2 x}}{121+25 x} \, dx,x,\log (x)\right )-2400000 \int \frac {1}{x^2 (121+25 \log (x))} \, dx+2400000 \text {Subst}\left (\int \frac {e^{-x}}{121+25 x} \, dx,x,\log (x)\right )-4000000 \text {Subst}\left (\int \frac {1}{x^2} \, dx,x,121+25 \log (x)\right )\\ &=96000 e^{121/25} \text {Ei}\left (\frac {1}{25} (-121-25 \log (x))\right )-324 e^{484/25} \text {Ei}\left (-\frac {4}{25} (121+25 \log (x))\right )+6480 e^{363/25} \text {Ei}\left (-\frac {3}{25} (121+25 \log (x))\right )-43200 e^{242/25} \text {Ei}\left (-\frac {2}{25} (121+25 \log (x))\right )+\frac {4000000}{121+25 \log (x)}+\frac {2025}{x^4 (121+25 \log (x))}-\frac {54000}{x^3 (121+25 \log (x))}+\frac {540000}{x^2 (121+25 \log (x))}-\frac {2400000}{x (121+25 \log (x))}+8100 \text {Subst}\left (\int \frac {e^{-4 x}}{121+25 x} \, dx,x,\log (x)\right )-162000 \text {Subst}\left (\int \frac {e^{-3 x}}{121+25 x} \, dx,x,\log (x)\right )+1080000 \text {Subst}\left (\int \frac {e^{-2 x}}{121+25 x} \, dx,x,\log (x)\right )-2400000 \text {Subst}\left (\int \frac {e^{-x}}{121+25 x} \, dx,x,\log (x)\right )\\ &=\frac {4000000}{121+25 \log (x)}+\frac {2025}{x^4 (121+25 \log (x))}-\frac {54000}{x^3 (121+25 \log (x))}+\frac {540000}{x^2 (121+25 \log (x))}-\frac {2400000}{x (121+25 \log (x))}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 20, normalized size = 1.11 \begin {gather*} \frac {25 (-3+20 x)^4}{x^4 (121+25 \log (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. \(63\) vs.
\(2(16)=32\).
time = 3.36, size = 64, normalized size = 3.56
method | result | size |
norman | \(\frac {4000000 x^{4}-2400000 x^{3}+540000 x^{2}-54000 x +2025}{x^{4} \left (121+25 \ln \left (x \right )\right )}\) | \(33\) |
risch | \(\frac {4000000 x^{4}-2400000 x^{3}+540000 x^{2}-54000 x +2025}{x^{4} \left (121+25 \ln \left (x \right )\right )}\) | \(34\) |
default | \(\frac {4000000}{121+25 \ln \left (x \right )}+\frac {2025}{x^{4} \left (121+25 \ln \left (x \right )\right )}-\frac {54000}{x^{3} \left (121+25 \ln \left (x \right )\right )}+\frac {540000}{x^{2} \left (121+25 \ln \left (x \right )\right )}-\frac {2400000}{x \left (121+25 \ln \left (x \right )\right )}\) | \(64\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 37, normalized size = 2.06 \begin {gather*} \frac {25 \, {\left (160000 \, x^{4} - 96000 \, x^{3} + 21600 \, x^{2} - 2160 \, x + 81\right )}}{25 \, x^{4} \log \left (x\right ) + 121 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 37, normalized size = 2.06 \begin {gather*} \frac {25 \, {\left (160000 \, x^{4} - 96000 \, x^{3} + 21600 \, x^{2} - 2160 \, x + 81\right )}}{25 \, x^{4} \log \left (x\right ) + 121 \, x^{4}} \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. 32 vs.
\(2 (12) = 24\).
time = 0.05, size = 32, normalized size = 1.78 \begin {gather*} \frac {4000000 x^{4} - 2400000 x^{3} + 540000 x^{2} - 54000 x + 2025}{25 x^{4} \log {\left (x \right )} + 121 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 37, normalized size = 2.06 \begin {gather*} \frac {25 \, {\left (160000 \, x^{4} - 96000 \, x^{3} + 21600 \, x^{2} - 2160 \, x + 81\right )}}{25 \, x^{4} \log \left (x\right ) + 121 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.37, size = 32, normalized size = 1.78 \begin {gather*} \frac {4000000\,x^4-2400000\,x^3+540000\,x^2-54000\,x+2025}{x^4\,\left (25\,\ln \left (x\right )+121\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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