Optimal. Leaf size=97 \[ \frac {16}{290521 (1-2 x)^2}+\frac {6464}{22370117 (1-2 x)}-\frac {27}{343 (2+3 x)^3}-\frac {3078}{2401 (2+3 x)^2}-\frac {333639}{16807 (2+3 x)}-\frac {15625}{1331 (3+5 x)}-\frac {761760 \log (1-2 x)}{1722499009}+\frac {15820110 \log (2+3 x)}{117649}-\frac {1968750 \log (3+5 x)}{14641} \]
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Rubi [A]
time = 0.04, antiderivative size = 97, 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 {6464}{22370117 (1-2 x)}-\frac {333639}{16807 (3 x+2)}-\frac {15625}{1331 (5 x+3)}+\frac {16}{290521 (1-2 x)^2}-\frac {3078}{2401 (3 x+2)^2}-\frac {27}{343 (3 x+2)^3}-\frac {761760 \log (1-2 x)}{1722499009}+\frac {15820110 \log (3 x+2)}{117649}-\frac {1968750 \log (5 x+3)}{14641} \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)^4 (3+5 x)^2} \, dx &=\int \left (-\frac {64}{290521 (-1+2 x)^3}+\frac {12928}{22370117 (-1+2 x)^2}-\frac {1523520}{1722499009 (-1+2 x)}+\frac {243}{343 (2+3 x)^4}+\frac {18468}{2401 (2+3 x)^3}+\frac {1000917}{16807 (2+3 x)^2}+\frac {47460330}{117649 (2+3 x)}+\frac {78125}{1331 (3+5 x)^2}-\frac {9843750}{14641 (3+5 x)}\right ) \, dx\\ &=\frac {16}{290521 (1-2 x)^2}+\frac {6464}{22370117 (1-2 x)}-\frac {27}{343 (2+3 x)^3}-\frac {3078}{2401 (2+3 x)^2}-\frac {333639}{16807 (2+3 x)}-\frac {15625}{1331 (3+5 x)}-\frac {761760 \log (1-2 x)}{1722499009}+\frac {15820110 \log (2+3 x)}{117649}-\frac {1968750 \log (3+5 x)}{14641}\\ \end {align*}
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Mathematica [A]
time = 0.11, size = 88, normalized size = 0.91 \begin {gather*} \frac {2 \left (\frac {77}{2} \left (\frac {1232}{(1-2 x)^2}+\frac {6464}{1-2 x}-\frac {1760913}{(2+3 x)^3}-\frac {28677726}{(2+3 x)^2}-\frac {444073509}{2+3 x}-\frac {262609375}{3+5 x}\right )-380880 \log (1-2 x)+115811115255 \log (4+6 x)-115810734375 \log (6+10 x)\right )}{1722499009} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 80, normalized size = 0.82
method | result | size |
risch | \(\frac {-\frac {108296789400}{22370117} x^{5}-\frac {14955760620}{3195731} x^{4}+\frac {46403447130}{22370117} x^{3}+\frac {55829767905}{22370117} x^{2}-\frac {4446481815}{22370117} x -\frac {7606921499}{22370117}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3} \left (3+5 x \right )}-\frac {761760 \ln \left (-1+2 x \right )}{1722499009}+\frac {15820110 \ln \left (2+3 x \right )}{117649}-\frac {1968750 \ln \left (3+5 x \right )}{14641}\) | \(74\) |
norman | \(\frac {-\frac {2119258905955}{536882808} x^{3}-\frac {586494185253}{178960936} x^{4}+\frac {23650340652}{3195731} x^{5}+\frac {84224259437}{268441404} x^{2}+\frac {342311467455}{44740234} x^{6}+\frac {72211088597}{134220702} x}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3} \left (3+5 x \right )}-\frac {761760 \ln \left (-1+2 x \right )}{1722499009}+\frac {15820110 \ln \left (2+3 x \right )}{117649}-\frac {1968750 \ln \left (3+5 x \right )}{14641}\) | \(77\) |
default | \(\frac {16}{290521 \left (-1+2 x \right )^{2}}-\frac {6464}{22370117 \left (-1+2 x \right )}-\frac {761760 \ln \left (-1+2 x \right )}{1722499009}-\frac {27}{343 \left (2+3 x \right )^{3}}-\frac {3078}{2401 \left (2+3 x \right )^{2}}-\frac {333639}{16807 \left (2+3 x \right )}+\frac {15820110 \ln \left (2+3 x \right )}{117649}-\frac {15625}{1331 \left (3+5 x \right )}-\frac {1968750 \ln \left (3+5 x \right )}{14641}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 84, normalized size = 0.87 \begin {gather*} -\frac {108296789400 \, x^{5} + 104690324340 \, x^{4} - 46403447130 \, x^{3} - 55829767905 \, x^{2} + 4446481815 \, x + 7606921499}{22370117 \, {\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )}} - \frac {1968750}{14641} \, \log \left (5 \, x + 3\right ) + \frac {15820110}{117649} \, \log \left (3 \, x + 2\right ) - \frac {761760}{1722499009} \, \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. 173 vs.
\(2 (79) = 158\).
time = 0.61, size = 173, normalized size = 1.78 \begin {gather*} -\frac {8338852783800 \, x^{5} + 8061154974180 \, x^{4} - 3573065429010 \, x^{3} - 4298892128685 \, x^{2} + 231621468750 \, {\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )} \log \left (5 \, x + 3\right ) - 231622230510 \, {\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )} \log \left (3 \, x + 2\right ) + 761760 \, {\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )} \log \left (2 \, x - 1\right ) + 342379099755 \, x + 585732955423}{1722499009 \, {\left (540 \, x^{6} + 864 \, x^{5} + 99 \, x^{4} - 425 \, x^{3} - 154 \, x^{2} + 52 \, x + 24\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 85, normalized size = 0.88 \begin {gather*} - \frac {108296789400 x^{5} + 104690324340 x^{4} - 46403447130 x^{3} - 55829767905 x^{2} + 4446481815 x + 7606921499}{12079863180 x^{6} + 19327781088 x^{5} + 2214641583 x^{4} - 9507299725 x^{3} - 3444998018 x^{2} + 1163246084 x + 536882808} - \frac {761760 \log {\left (x - \frac {1}{2} \right )}}{1722499009} - \frac {1968750 \log {\left (x + \frac {3}{5} \right )}}{14641} + \frac {15820110 \log {\left (x + \frac {2}{3} \right )}}{117649} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.74, size = 104, normalized size = 1.07 \begin {gather*} -\frac {15625}{1331 \, {\left (5 \, x + 3\right )}} - \frac {25 \, {\left (\frac {1535578147116}{5 \, x + 3} - \frac {3297944687832}{{\left (5 \, x + 3\right )}^{2}} - \frac {3224232263641}{{\left (5 \, x + 3\right )}^{3}} - \frac {689127341628}{{\left (5 \, x + 3\right )}^{4}} - 150040675728\right )}}{246071287 \, {\left (\frac {11}{5 \, x + 3} - 2\right )}^{2} {\left (\frac {1}{5 \, x + 3} + 3\right )}^{3}} + \frac {15820110}{117649} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {761760}{1722499009} \, \log \left ({\left | -\frac {11}{5 \, x + 3} + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 76, normalized size = 0.78 \begin {gather*} \frac {15820110\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {761760\,\ln \left (x-\frac {1}{2}\right )}{1722499009}-\frac {1968750\,\ln \left (x+\frac {3}{5}\right )}{14641}-\frac {\frac {200549610\,x^5}{22370117}+\frac {27695853\,x^4}{3195731}-\frac {171864619\,x^3}{44740234}-\frac {1240661509\,x^2}{268441404}+\frac {98810707\,x}{268441404}+\frac {7606921499}{12079863180}}{x^6+\frac {8\,x^5}{5}+\frac {11\,x^4}{60}-\frac {85\,x^3}{108}-\frac {77\,x^2}{270}+\frac {13\,x}{135}+\frac {2}{45}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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