Optimal. Leaf size=75 \[ \frac {16}{41503 (1-2 x)}-\frac {27}{98 (2+3 x)^2}-\frac {1998}{343 (2+3 x)}-\frac {625}{121 (3+5 x)}-\frac {2704 \log (1-2 x)}{3195731}+\frac {107109 \log (2+3 x)}{2401}-\frac {59375 \log (3+5 x)}{1331} \]
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Rubi [A]
time = 0.03, antiderivative size = 75, 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 {16}{41503 (1-2 x)}-\frac {1998}{343 (3 x+2)}-\frac {625}{121 (5 x+3)}-\frac {27}{98 (3 x+2)^2}-\frac {2704 \log (1-2 x)}{3195731}+\frac {107109 \log (3 x+2)}{2401}-\frac {59375 \log (5 x+3)}{1331} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {1}{(1-2 x)^2 (2+3 x)^3 (3+5 x)^2} \, dx &=\int \left (\frac {32}{41503 (-1+2 x)^2}-\frac {5408}{3195731 (-1+2 x)}+\frac {81}{49 (2+3 x)^3}+\frac {5994}{343 (2+3 x)^2}+\frac {321327}{2401 (2+3 x)}+\frac {3125}{121 (3+5 x)^2}-\frac {296875}{1331 (3+5 x)}\right ) \, dx\\ &=\frac {16}{41503 (1-2 x)}-\frac {27}{98 (2+3 x)^2}-\frac {1998}{343 (2+3 x)}-\frac {625}{121 (3+5 x)}-\frac {2704 \log (1-2 x)}{3195731}+\frac {107109 \log (2+3 x)}{2401}-\frac {59375 \log (3+5 x)}{1331}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 65, normalized size = 0.87 \begin {gather*} \frac {-\frac {77 \left (-4684319-5074951 x+17783592 x^2+22224420 x^3\right )}{(2+3 x)^2 \left (-3+x+10 x^2\right )}-5408 \log (3-6 x)+285124158 \log (2+3 x)-285118750 \log (-3 (3+5 x))}{6391462} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 62, normalized size = 0.83
method | result | size |
default | \(-\frac {16}{41503 \left (-1+2 x \right )}-\frac {2704 \ln \left (-1+2 x \right )}{3195731}-\frac {27}{98 \left (2+3 x \right )^{2}}-\frac {1998}{343 \left (2+3 x \right )}+\frac {107109 \ln \left (2+3 x \right )}{2401}-\frac {625}{121 \left (3+5 x \right )}-\frac {59375 \ln \left (3+5 x \right )}{1331}\) | \(62\) |
risch | \(\frac {-\frac {11112210}{41503} x^{3}-\frac {8891796}{41503} x^{2}+\frac {724993}{11858} x +\frac {4684319}{83006}}{\left (-1+2 x \right ) \left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {2704 \ln \left (-1+2 x \right )}{3195731}+\frac {107109 \ln \left (2+3 x \right )}{2401}-\frac {59375 \ln \left (3+5 x \right )}{1331}\) | \(64\) |
norman | \(\frac {\frac {112528037}{332024} x^{3}-\frac {13756447}{142296} x^{2}+\frac {70264785}{166012} x^{4}-\frac {22249699}{249018} x}{\left (-1+2 x \right ) \left (2+3 x \right )^{2} \left (3+5 x \right )}-\frac {2704 \ln \left (-1+2 x \right )}{3195731}+\frac {107109 \ln \left (2+3 x \right )}{2401}-\frac {59375 \ln \left (3+5 x \right )}{1331}\) | \(67\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.36, size = 64, normalized size = 0.85 \begin {gather*} -\frac {22224420 \, x^{3} + 17783592 \, x^{2} - 5074951 \, x - 4684319}{83006 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} - \frac {59375}{1331} \, \log \left (5 \, x + 3\right ) + \frac {107109}{2401} \, \log \left (3 \, x + 2\right ) - \frac {2704}{3195731} \, \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. 123 vs.
\(2 (61) = 122\).
time = 0.57, size = 123, normalized size = 1.64 \begin {gather*} -\frac {1711280340 \, x^{3} + 1369336584 \, x^{2} + 285118750 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (5 \, x + 3\right ) - 285124158 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (3 \, x + 2\right ) + 5408 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )} \log \left (2 \, x - 1\right ) - 390771227 \, x - 360692563}{6391462 \, {\left (90 \, x^{4} + 129 \, x^{3} + 25 \, x^{2} - 32 \, x - 12\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.11, size = 65, normalized size = 0.87 \begin {gather*} \frac {- 22224420 x^{3} - 17783592 x^{2} + 5074951 x + 4684319}{7470540 x^{4} + 10707774 x^{3} + 2075150 x^{2} - 2656192 x - 996072} - \frac {2704 \log {\left (x - \frac {1}{2} \right )}}{3195731} - \frac {59375 \log {\left (x + \frac {3}{5} \right )}}{1331} + \frac {107109 \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 = 0.83, size = 86, normalized size = 1.15 \begin {gather*} -\frac {625}{121 \, {\left (5 \, x + 3\right )}} + \frac {5 \, {\left (\frac {604065417}{5 \, x + 3} + \frac {258530842}{{\left (5 \, x + 3\right )}^{2}} - 118375902\right )}}{913066 \, {\left (\frac {11}{5 \, x + 3} - 2\right )} {\left (\frac {1}{5 \, x + 3} + 3\right )}^{2}} + \frac {107109}{2401} \, \log \left ({\left | -\frac {1}{5 \, x + 3} - 3 \right |}\right ) - \frac {2704}{3195731} \, \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 = 55, normalized size = 0.73 \begin {gather*} \frac {107109\,\ln \left (x+\frac {2}{3}\right )}{2401}-\frac {2704\,\ln \left (x-\frac {1}{2}\right )}{3195731}-\frac {59375\,\ln \left (x+\frac {3}{5}\right )}{1331}+\frac {-\frac {123469\,x^3}{41503}-\frac {1481966\,x^2}{622545}+\frac {724993\,x}{1067220}+\frac {4684319}{7470540}}{x^4+\frac {43\,x^3}{30}+\frac {5\,x^2}{18}-\frac {16\,x}{45}-\frac {2}{15}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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