Optimal. Leaf size=81 \[ \frac {343}{162 (2+3 x)^6}+\frac {1421}{135 (2+3 x)^5}+\frac {7189}{108 (2+3 x)^4}+\frac {1331}{3 (2+3 x)^3}+\frac {6655}{2 (2+3 x)^2}+\frac {33275}{2+3 x}-166375 \log (2+3 x)+166375 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 81, 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 {33275}{3 x+2}+\frac {6655}{2 (3 x+2)^2}+\frac {1331}{3 (3 x+2)^3}+\frac {7189}{108 (3 x+2)^4}+\frac {1421}{135 (3 x+2)^5}+\frac {343}{162 (3 x+2)^6}-166375 \log (3 x+2)+166375 \log (5 x+3) \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^3}{(2+3 x)^7 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^7}-\frac {1421}{9 (2+3 x)^6}-\frac {7189}{9 (2+3 x)^5}-\frac {3993}{(2+3 x)^4}-\frac {19965}{(2+3 x)^3}-\frac {99825}{(2+3 x)^2}-\frac {499125}{2+3 x}+\frac {831875}{3+5 x}\right ) \, dx\\ &=\frac {343}{162 (2+3 x)^6}+\frac {1421}{135 (2+3 x)^5}+\frac {7189}{108 (2+3 x)^4}+\frac {1331}{3 (2+3 x)^3}+\frac {6655}{2 (2+3 x)^2}+\frac {33275}{2+3 x}-166375 \log (2+3 x)+166375 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 75, normalized size = 0.93 \begin {gather*} \frac {3430+17052 (2+3 x)+107835 (2+3 x)^2+718740 (2+3 x)^3+5390550 (2+3 x)^4+53905500 (2+3 x)^5}{1620 (2+3 x)^6}-166375 \log (5 (2+3 x))+166375 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 72, normalized size = 0.89
method | result | size |
risch | \(\frac {8085825 x^{5}+\frac {54444555}{2} x^{4}+36667719 x^{3}+\frac {296415565}{12} x^{2}+\frac {374500906}{45} x +\frac {908721797}{810}}{\left (2+3 x \right )^{6}}-166375 \ln \left (2+3 x \right )+166375 \ln \left (3+5 x \right )\) | \(52\) |
norman | \(\frac {-\frac {3549333}{2} x -\frac {468709169}{12} x^{3}-\frac {105296889}{8} x^{2}-\frac {6884764173}{160} x^{5}-\frac {8178496173}{640} x^{6}-\frac {1855052511}{32} x^{4}}{\left (2+3 x \right )^{6}}-166375 \ln \left (2+3 x \right )+166375 \ln \left (3+5 x \right )\) | \(55\) |
default | \(\frac {343}{162 \left (2+3 x \right )^{6}}+\frac {1421}{135 \left (2+3 x \right )^{5}}+\frac {7189}{108 \left (2+3 x \right )^{4}}+\frac {1331}{3 \left (2+3 x \right )^{3}}+\frac {6655}{2 \left (2+3 x \right )^{2}}+\frac {33275}{2+3 x}-166375 \ln \left (2+3 x \right )+166375 \ln \left (3+5 x \right )\) | \(72\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 76, normalized size = 0.94 \begin {gather*} \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} + 166375 \, \log \left (5 \, x + 3\right ) - 166375 \, \log \left (3 \, x + 2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 135, normalized size = 1.67 \begin {gather*} \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 269527500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (5 \, x + 3\right ) - 269527500 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )} \log \left (3 \, x + 2\right ) + 13482032616 \, x + 1817443594}{1620 \, {\left (729 \, x^{6} + 2916 \, x^{5} + 4860 \, x^{4} + 4320 \, x^{3} + 2160 \, x^{2} + 576 \, x + 64\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 73, normalized size = 0.90 \begin {gather*} - \frac {- 13099036500 x^{5} - 44100089550 x^{4} - 59401704780 x^{3} - 40016101275 x^{2} - 13482032616 x - 1817443594}{1180980 x^{6} + 4723920 x^{5} + 7873200 x^{4} + 6998400 x^{3} + 3499200 x^{2} + 933120 x + 103680} + 166375 \log {\left (x + \frac {3}{5} \right )} - 166375 \log {\left (x + \frac {2}{3} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.59, size = 53, normalized size = 0.65 \begin {gather*} \frac {13099036500 \, x^{5} + 44100089550 \, x^{4} + 59401704780 \, x^{3} + 40016101275 \, x^{2} + 13482032616 \, x + 1817443594}{1620 \, {\left (3 \, x + 2\right )}^{6}} + 166375 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 166375 \, \log \left ({\left | 3 \, x + 2 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.12, size = 65, normalized size = 0.80 \begin {gather*} \frac {\frac {33275\,x^5}{3}+\frac {672155\,x^4}{18}+\frac {4074191\,x^3}{81}+\frac {296415565\,x^2}{8748}+\frac {374500906\,x}{32805}+\frac {908721797}{590490}}{x^6+4\,x^5+\frac {20\,x^4}{3}+\frac {160\,x^3}{27}+\frac {80\,x^2}{27}+\frac {64\,x}{81}+\frac {64}{729}}-332750\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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