Optimal. Leaf size=86 \[ \frac {8}{65219 (1-2 x)^2}+\frac {2736}{5021863 (1-2 x)}+\frac {243}{343 (2+3 x)}-\frac {625}{2662 (3+5 x)^2}+\frac {37500}{14641 (3+5 x)}-\frac {280752 \log (1-2 x)}{386683451}-\frac {26973 \log (2+3 x)}{2401}+\frac {1809375 \log (3+5 x)}{161051} \]
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Rubi [A]
time = 0.03, antiderivative size = 86, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.045, Rules used = {90}
\begin {gather*} \frac {2736}{5021863 (1-2 x)}+\frac {243}{343 (3 x+2)}+\frac {37500}{14641 (5 x+3)}+\frac {8}{65219 (1-2 x)^2}-\frac {625}{2662 (5 x+3)^2}-\frac {280752 \log (1-2 x)}{386683451}-\frac {26973 \log (3 x+2)}{2401}+\frac {1809375 \log (5 x+3)}{161051} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^3 (2+3 x)^2 (3+5 x)^3} \, dx &=\int \left (-\frac {32}{65219 (-1+2 x)^3}+\frac {5472}{5021863 (-1+2 x)^2}-\frac {561504}{386683451 (-1+2 x)}-\frac {729}{343 (2+3 x)^2}-\frac {80919}{2401 (2+3 x)}+\frac {3125}{1331 (3+5 x)^3}-\frac {187500}{14641 (3+5 x)^2}+\frac {9046875}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {8}{65219 (1-2 x)^2}+\frac {2736}{5021863 (1-2 x)}+\frac {243}{343 (2+3 x)}-\frac {625}{2662 (3+5 x)^2}+\frac {37500}{14641 (3+5 x)}-\frac {280752 \log (1-2 x)}{386683451}-\frac {26973 \log (2+3 x)}{2401}+\frac {1809375 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 76, normalized size = 0.88 \begin {gather*} -\frac {3 \left (-\frac {182631834}{2+3 x}-\frac {65219 (-6101+12290 x)}{3 \left (-3+x+10 x^2\right )^2}-\frac {154 (-4446931+8570440 x)}{-3+x+10 x^2}+187168 \log (3-6 x)+2896019082 \log (2+3 x)-2896206250 \log (-3 (3+5 x))\right )}{773366902} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 71, normalized size = 0.83
method | result | size |
risch | \(\frac {\frac {1127115900}{5021863} x^{4}+\frac {262291830}{5021863} x^{3}-\frac {681111051}{5021863} x^{2}-\frac {159141275}{10043726} x +\frac {106897078}{5021863}}{\left (-1+2 x \right )^{2} \left (2+3 x \right ) \left (3+5 x \right )^{2}}-\frac {280752 \ln \left (-1+2 x \right )}{386683451}-\frac {26973 \ln \left (2+3 x \right )}{2401}+\frac {1809375 \ln \left (3+5 x \right )}{161051}\) | \(69\) |
norman | \(\frac {-\frac {601093499}{2152227} x^{2}+\frac {1591412750}{5021863} x^{5}-\frac {2786719955}{30131178} x^{3}+\frac {683547350}{1369599} x^{4}+\frac {202381843}{5021863}}{\left (-1+2 x \right )^{2} \left (2+3 x \right ) \left (3+5 x \right )^{2}}-\frac {280752 \ln \left (-1+2 x \right )}{386683451}-\frac {26973 \ln \left (2+3 x \right )}{2401}+\frac {1809375 \ln \left (3+5 x \right )}{161051}\) | \(70\) |
default | \(\frac {8}{65219 \left (-1+2 x \right )^{2}}-\frac {2736}{5021863 \left (-1+2 x \right )}-\frac {280752 \ln \left (-1+2 x \right )}{386683451}+\frac {243}{343 \left (2+3 x \right )}-\frac {26973 \ln \left (2+3 x \right )}{2401}-\frac {625}{2662 \left (3+5 x \right )^{2}}+\frac {37500}{14641 \left (3+5 x \right )}+\frac {1809375 \ln \left (3+5 x \right )}{161051}\) | \(71\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 74, normalized size = 0.86 \begin {gather*} \frac {2254231800 \, x^{4} + 524583660 \, x^{3} - 1362222102 \, x^{2} - 159141275 \, x + 213794156}{10043726 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )}} + \frac {1809375}{161051} \, \log \left (5 \, x + 3\right ) - \frac {26973}{2401} \, \log \left (3 \, x + 2\right ) - \frac {280752}{386683451} \, \log \left (2 \, x - 1\right ) \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. 148 vs.
\(2 (70) = 140\).
time = 1.17, size = 148, normalized size = 1.72 \begin {gather*} \frac {173575848600 \, x^{4} + 40392941820 \, x^{3} - 104891101854 \, x^{2} + 8688618750 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (5 \, x + 3\right ) - 8688057246 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (3 \, x + 2\right ) - 561504 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )} \log \left (2 \, x - 1\right ) - 12253878175 \, x + 16462150012}{773366902 \, {\left (300 \, x^{5} + 260 \, x^{4} - 137 \, x^{3} - 136 \, x^{2} + 15 \, x + 18\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.15, size = 75, normalized size = 0.87 \begin {gather*} - \frac {- 2254231800 x^{4} - 524583660 x^{3} + 1362222102 x^{2} + 159141275 x - 213794156}{3013117800 x^{5} + 2611368760 x^{4} - 1375990462 x^{3} - 1365946736 x^{2} + 150655890 x + 180787068} - \frac {280752 \log {\left (x - \frac {1}{2} \right )}}{386683451} + \frac {1809375 \log {\left (x + \frac {3}{5} \right )}}{161051} - \frac {26973 \log {\left (x + \frac {2}{3} \right )}}{2401} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.58, size = 95, normalized size = 1.10 \begin {gather*} \frac {243}{343 \, {\left (3 \, x + 2\right )}} - \frac {9 \, {\left (\frac {55432245900}{3 \, x + 2} - \frac {106776659235}{{\left (3 \, x + 2\right )}^{2}} + \frac {22794463286}{{\left (3 \, x + 2\right )}^{3}} - 7652987500\right )}}{70306082 \, {\left (\frac {7}{3 \, x + 2} - 2\right )}^{2} {\left (\frac {1}{3 \, x + 2} - 5\right )}^{2}} + \frac {1809375}{161051} \, \log \left ({\left | -\frac {1}{3 \, x + 2} + 5 \right |}\right ) - \frac {280752}{386683451} \, \log \left ({\left | -\frac {7}{3 \, x + 2} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 65, normalized size = 0.76 \begin {gather*} \frac {1809375\,\ln \left (x+\frac {3}{5}\right )}{161051}-\frac {26973\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {280752\,\ln \left (x-\frac {1}{2}\right )}{386683451}+\frac {\frac {3757053\,x^4}{5021863}+\frac {8743061\,x^3}{50218630}-\frac {227037017\,x^2}{502186300}-\frac {6365651\,x}{120524712}+\frac {53448539}{753279450}}{x^5+\frac {13\,x^4}{15}-\frac {137\,x^3}{300}-\frac {34\,x^2}{75}+\frac {x}{20}+\frac {3}{50}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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