Optimal. Leaf size=65 \[ \frac {343}{5324 (1-2 x)^2}+\frac {147}{14641 (1-2 x)}-\frac {1}{13310 (3+5 x)^2}-\frac {21}{14641 (3+5 x)}-\frac {777 \log (1-2 x)}{161051}+\frac {777 \log (3+5 x)}{161051} \]
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Rubi [A]
time = 0.02, antiderivative size = 65, 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 {147}{14641 (1-2 x)}-\frac {21}{14641 (5 x+3)}+\frac {343}{5324 (1-2 x)^2}-\frac {1}{13310 (5 x+3)^2}-\frac {777 \log (1-2 x)}{161051}+\frac {777 \log (5 x+3)}{161051} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(2+3 x)^3}{(1-2 x)^3 (3+5 x)^3} \, dx &=\int \left (-\frac {343}{1331 (-1+2 x)^3}+\frac {294}{14641 (-1+2 x)^2}-\frac {1554}{161051 (-1+2 x)}+\frac {1}{1331 (3+5 x)^3}+\frac {105}{14641 (3+5 x)^2}+\frac {3885}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {343}{5324 (1-2 x)^2}+\frac {147}{14641 (1-2 x)}-\frac {1}{13310 (3+5 x)^2}-\frac {21}{14641 (3+5 x)}-\frac {777 \log (1-2 x)}{161051}+\frac {777 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A]
time = 0.03, size = 48, normalized size = 0.74 \begin {gather*} \frac {-\frac {11 \left (-194963-604258 x-371997 x^2+155400 x^3\right )}{\left (-3+x+10 x^2\right )^2}+15540 \log (-3-5 x)-15540 \log (1-2 x)}{3221020} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 54, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {7770}{14641} x^{3}+\frac {371997}{292820} x^{2}+\frac {302129}{146410} x +\frac {194963}{292820}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {777 \ln \left (-1+2 x \right )}{161051}+\frac {777 \ln \left (3+5 x \right )}{161051}\) | \(49\) |
norman | \(\frac {-\frac {835481}{43923} x^{2}+\frac {1510645}{43923} x^{4}+\frac {278819}{43923} x^{3}+\frac {110135}{29282}}{\left (-1+2 x \right )^{2} \left (3+5 x \right )^{2}}-\frac {777 \ln \left (-1+2 x \right )}{161051}+\frac {777 \ln \left (3+5 x \right )}{161051}\) | \(50\) |
default | \(\frac {343}{5324 \left (-1+2 x \right )^{2}}-\frac {147}{14641 \left (-1+2 x \right )}-\frac {777 \ln \left (-1+2 x \right )}{161051}-\frac {1}{13310 \left (3+5 x \right )^{2}}-\frac {21}{14641 \left (3+5 x \right )}+\frac {777 \ln \left (3+5 x \right )}{161051}\) | \(54\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.41, size = 56, normalized size = 0.86 \begin {gather*} -\frac {155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} + \frac {777}{161051} \, \log \left (5 \, x + 3\right ) - \frac {777}{161051} \, \log \left (2 \, x - 1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.58, size = 95, normalized size = 1.46 \begin {gather*} -\frac {1709400 \, x^{3} - 4091967 \, x^{2} - 15540 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (5 \, x + 3\right ) + 15540 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )} \log \left (2 \, x - 1\right ) - 6646838 \, x - 2144593}{3221020 \, {\left (100 \, x^{4} + 20 \, x^{3} - 59 \, x^{2} - 6 \, x + 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 54, normalized size = 0.83 \begin {gather*} - \frac {155400 x^{3} - 371997 x^{2} - 604258 x - 194963}{29282000 x^{4} + 5856400 x^{3} - 17276380 x^{2} - 1756920 x + 2635380} - \frac {777 \log {\left (x - \frac {1}{2} \right )}}{161051} + \frac {777 \log {\left (x + \frac {3}{5} \right )}}{161051} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.69, size = 46, normalized size = 0.71 \begin {gather*} -\frac {155400 \, x^{3} - 371997 \, x^{2} - 604258 \, x - 194963}{292820 \, {\left (10 \, x^{2} + x - 3\right )}^{2}} + \frac {777}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {777}{161051} \, \log \left ({\left | 2 \, x - 1 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.07, size = 45, normalized size = 0.69 \begin {gather*} \frac {1554\,\mathrm {atanh}\left (\frac {20\,x}{11}+\frac {1}{11}\right )}{161051}+\frac {-\frac {777\,x^3}{146410}+\frac {371997\,x^2}{29282000}+\frac {302129\,x}{14641000}+\frac {194963}{29282000}}{x^4+\frac {x^3}{5}-\frac {59\,x^2}{100}-\frac {3\,x}{50}+\frac {9}{100}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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