Optimal. Leaf size=64 \[ -\frac {9}{14 (2+3 x)^2}-\frac {648}{49 (2+3 x)}-\frac {125}{11 (3+5 x)}-\frac {16 \log (1-2 x)}{41503}+\frac {34371}{343} \log (2+3 x)-\frac {12125}{121} \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 64, 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 {648}{49 (3 x+2)}-\frac {125}{11 (5 x+3)}-\frac {9}{14 (3 x+2)^2}-\frac {16 \log (1-2 x)}{41503}+\frac {34371}{343} \log (3 x+2)-\frac {12125}{121} \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x) (2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (-\frac {32}{41503 (-1+2 x)}+\frac {27}{7 (2+3 x)^3}+\frac {1944}{49 (2+3 x)^2}+\frac {103113}{343 (2+3 x)}+\frac {625}{11 (3+5 x)^2}-\frac {60625}{121 (3+5 x)}\right ) \, dx\\ &=-\frac {9}{14 (2+3 x)^2}-\frac {648}{49 (2+3 x)}-\frac {125}{11 (3+5 x)}-\frac {16 \log (1-2 x)}{41503}+\frac {34371}{343} \log (2+3 x)-\frac {12125}{121} \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.02, size = 60, normalized size = 0.94 \begin {gather*} -\frac {9}{14 (2+3 x)^2}-\frac {125}{33+55 x}-\frac {648}{98+147 x}-\frac {16 \log (1-2 x)}{41503}+\frac {34371}{343} \log (4+6 x)-\frac {12125}{121} \log (6+10 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 53, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {162045}{539} x^{2}-\frac {421329}{1078} x -\frac {136615}{1078}}{\left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {16 \ln \left (-1+2 x \right )}{41503}+\frac {34371 \ln \left (2+3 x \right )}{343}-\frac {12125 \ln \left (3+5 x \right )}{121}\) | \(52\) |
default | \(-\frac {16 \ln \left (-1+2 x \right )}{41503}-\frac {9}{14 \left (2+3 x \right )^{2}}-\frac {648}{49 \left (2+3 x \right )}+\frac {34371 \ln \left (2+3 x \right )}{343}-\frac {125}{11 \left (3+5 x \right )}-\frac {12125 \ln \left (3+5 x \right )}{121}\) | \(53\) |
norman | \(\frac {\frac {648623}{3234} x +\frac {2049225}{4312} x^{3}+\frac {2665475}{4312} x^{2}}{\left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {16 \ln \left (-1+2 x \right )}{41503}+\frac {34371 \ln \left (2+3 x \right )}{343}-\frac {12125 \ln \left (3+5 x \right )}{121}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 54, normalized size = 0.84 \begin {gather*} -\frac {324090 \, x^{2} + 421329 \, x + 136615}{1078 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )}} - \frac {12125}{121} \, \log \left (5 \, x + 3\right ) + \frac {34371}{343} \, \log \left (3 \, x + 2\right ) - \frac {16}{41503} \, \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 = 0.72, size = 98, normalized size = 1.53 \begin {gather*} -\frac {24954930 \, x^{2} + 8317750 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (5 \, x + 3\right ) - 8317782 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (3 \, x + 2\right ) + 32 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\right )} \log \left (2 \, x - 1\right ) + 32442333 \, x + 10519355}{83006 \, {\left (45 \, x^{3} + 87 \, x^{2} + 56 \, x + 12\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 = 0.84 \begin {gather*} - \frac {324090 x^{2} + 421329 x + 136615}{48510 x^{3} + 93786 x^{2} + 60368 x + 12936} - \frac {16 \log {\left (x - \frac {1}{2} \right )}}{41503} - \frac {12125 \log {\left (x + \frac {3}{5} \right )}}{121} + \frac {34371 \log {\left (x + \frac {2}{3} \right )}}{343} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.76, size = 64, normalized size = 1.00 \begin {gather*} -\frac {125}{11 \, {\left (5 \, x + 3\right )}} + \frac {135 \, {\left (\frac {214}{5 \, x + 3} + 537\right )}}{98 \, {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + \frac {34371}{343} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {16}{41503} \, \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 = 0.04, size = 46, normalized size = 0.72 \begin {gather*} \frac {34371\,\ln \left (x+\frac {2}{3}\right )}{343}-\frac {16\,\ln \left (x-\frac {1}{2}\right )}{41503}-\frac {12125\,\ln \left (x+\frac {3}{5}\right )}{121}-\frac {\frac {3601\,x^2}{539}+\frac {140443\,x}{16170}+\frac {27323}{9702}}{x^3+\frac {29\,x^2}{15}+\frac {56\,x}{45}+\frac {4}{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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