Optimal. Leaf size=108 \[ \frac {32}{3195731 (1-2 x)^2}+\frac {15168}{246071287 (1-2 x)}+\frac {81}{343 (2+3 x)^3}+\frac {26973}{4802 (2+3 x)^2}+\frac {1944972}{16807 (2+3 x)}-\frac {15625}{2662 (3+5 x)^2}+\frac {1968750}{14641 (3+5 x)}-\frac {2054400 \log (1-2 x)}{18947489099}-\frac {115534350 \log (2+3 x)}{117649}+\frac {158156250 \log (3+5 x)}{161051} \]
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Rubi [A]
time = 0.04, antiderivative size = 108, 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 {15168}{246071287 (1-2 x)}+\frac {1944972}{16807 (3 x+2)}+\frac {1968750}{14641 (5 x+3)}+\frac {32}{3195731 (1-2 x)^2}+\frac {26973}{4802 (3 x+2)^2}-\frac {15625}{2662 (5 x+3)^2}+\frac {81}{343 (3 x+2)^3}-\frac {2054400 \log (1-2 x)}{18947489099}-\frac {115534350 \log (3 x+2)}{117649}+\frac {158156250 \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)^4 (3+5 x)^3} \, dx &=\int \left (-\frac {128}{3195731 (-1+2 x)^3}+\frac {30336}{246071287 (-1+2 x)^2}-\frac {4108800}{18947489099 (-1+2 x)}-\frac {729}{343 (2+3 x)^4}-\frac {80919}{2401 (2+3 x)^3}-\frac {5834916}{16807 (2+3 x)^2}-\frac {346603050}{117649 (2+3 x)}+\frac {78125}{1331 (3+5 x)^3}-\frac {9843750}{14641 (3+5 x)^2}+\frac {790781250}{161051 (3+5 x)}\right ) \, dx\\ &=\frac {32}{3195731 (1-2 x)^2}+\frac {15168}{246071287 (1-2 x)}+\frac {81}{343 (2+3 x)^3}+\frac {26973}{4802 (2+3 x)^2}+\frac {1944972}{16807 (2+3 x)}-\frac {15625}{2662 (3+5 x)^2}+\frac {1968750}{14641 (3+5 x)}-\frac {2054400 \log (1-2 x)}{18947489099}-\frac {115534350 \log (2+3 x)}{117649}+\frac {158156250 \log (3+5 x)}{161051}\\ \end {align*}
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Mathematica [A]
time = 0.09, size = 82, normalized size = 0.76 \begin {gather*} -\frac {3 \left (-\frac {77 \left (3666255393392+8254486652965 x-23334840827100 x^2-67213599053550 x^3+13177709631900 x^4+136289326113000 x^5+86993245890000 x^6\right )}{3 (2+3 x)^3 \left (-3+x+10 x^2\right )^2}+1369600 \log (3-6 x)+12404615067900 \log (2+3 x)-12404616437500 \log (-3 (3+5 x))\right )}{37894978198} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 89, normalized size = 0.82
method | result | size |
risch | \(\frac {\frac {43496622945000}{246071287} x^{6}+\frac {68144663056500}{246071287} x^{5}+\frac {598986801450}{22370117} x^{4}-\frac {33606799526775}{246071287} x^{3}-\frac {1060674583050}{22370117} x^{2}+\frac {3437936965}{204974} x +\frac {1833127696696}{246071287}}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-\frac {2054400 \ln \left (-1+2 x \right )}{18947489099}-\frac {115534350 \ln \left (2+3 x \right )}{117649}+\frac {158156250 \ln \left (3+5 x \right )}{161051}\) | \(79\) |
norman | \(\frac {-\frac {107736412032420}{246071287} x^{6}-\frac {68742288626100}{246071287} x^{7}-\frac {1198373660824}{45196767} x^{2}-\frac {950062449031}{22370117} x^{5}+\frac {15102915611540}{201331053} x^{3}+\frac {478169372038586}{2214641583} x^{4}-\frac {17398477065113}{1476427722} x}{\left (-1+2 x \right )^{2} \left (2+3 x \right )^{3} \left (3+5 x \right )^{2}}-\frac {2054400 \ln \left (-1+2 x \right )}{18947489099}-\frac {115534350 \ln \left (2+3 x \right )}{117649}+\frac {158156250 \ln \left (3+5 x \right )}{161051}\) | \(82\) |
default | \(\frac {32}{3195731 \left (-1+2 x \right )^{2}}-\frac {15168}{246071287 \left (-1+2 x \right )}-\frac {2054400 \ln \left (-1+2 x \right )}{18947489099}+\frac {81}{343 \left (2+3 x \right )^{3}}+\frac {26973}{4802 \left (2+3 x \right )^{2}}+\frac {1944972}{16807 \left (2+3 x \right )}-\frac {115534350 \ln \left (2+3 x \right )}{117649}-\frac {15625}{2662 \left (3+5 x \right )^{2}}+\frac {1968750}{14641 \left (3+5 x \right )}+\frac {158156250 \ln \left (3+5 x \right )}{161051}\) | \(89\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 94, normalized size = 0.87 \begin {gather*} \frac {86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} + \frac {158156250}{161051} \, \log \left (5 \, x + 3\right ) - \frac {115534350}{117649} \, \log \left (3 \, x + 2\right ) - \frac {2054400}{18947489099} \, \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. 198 vs.
\(2 (88) = 176\).
time = 0.71, size = 198, normalized size = 1.83 \begin {gather*} \frac {6698479933530000 \, x^{6} + 10494278110701000 \, x^{5} + 1014683641656300 \, x^{4} - 5175447127123350 \, x^{3} - 1796782743686700 \, x^{2} + 37213849312500 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (5 \, x + 3\right ) - 37213845203700 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (3 \, x + 2\right ) - 4108800 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )} \log \left (2 \, x - 1\right ) + 635595472278305 \, x + 282301665291184}{37894978198 \, {\left (2700 \, x^{7} + 5940 \, x^{6} + 3087 \, x^{5} - 1828 \, x^{4} - 2045 \, x^{3} - 202 \, x^{2} + 276 \, x + 72\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.14, size = 95, normalized size = 0.88 \begin {gather*} - \frac {- 86993245890000 x^{6} - 136289326113000 x^{5} - 13177709631900 x^{4} + 67213599053550 x^{3} + 23334840827100 x^{2} - 8254486652965 x - 3666255393392}{1328784949800 x^{7} + 2923326889560 x^{6} + 1519244125938 x^{5} - 899636625272 x^{4} - 1006431563830 x^{3} - 99412799948 x^{2} + 135831350424 x + 35434265328} - \frac {2054400 \log {\left (x - \frac {1}{2} \right )}}{18947489099} + \frac {158156250 \log {\left (x + \frac {3}{5} \right )}}{161051} - \frac {115534350 \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 = 0.56, size = 81, normalized size = 0.75 \begin {gather*} \frac {86993245890000 \, x^{6} + 136289326113000 \, x^{5} + 13177709631900 \, x^{4} - 67213599053550 \, x^{3} - 23334840827100 \, x^{2} + 8254486652965 \, x + 3666255393392}{492142574 \, {\left (5 \, x + 3\right )}^{2} {\left (3 \, x + 2\right )}^{3} {\left (2 \, x - 1\right )}^{2}} + \frac {158156250}{161051} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - \frac {115534350}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {2054400}{18947489099} \, \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 = 0.05, size = 85, normalized size = 0.79 \begin {gather*} \frac {158156250\,\ln \left (x+\frac {3}{5}\right )}{161051}-\frac {115534350\,\ln \left (x+\frac {2}{3}\right )}{117649}-\frac {2054400\,\ln \left (x-\frac {1}{2}\right )}{18947489099}+\frac {\frac {16109860350\,x^6}{246071287}+\frac {25238764095\,x^5}{246071287}+\frac {443693927\,x^4}{44740234}-\frac {448090660357\,x^3}{8858566332}-\frac {2357054629\,x^2}{134220702}+\frac {687587393\,x}{110685960}+\frac {458281924174}{166098118725}}{x^7+\frac {11\,x^6}{5}+\frac {343\,x^5}{300}-\frac {457\,x^4}{675}-\frac {409\,x^3}{540}-\frac {101\,x^2}{1350}+\frac {23\,x}{225}+\frac {2}{75}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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