Optimal. Leaf size=70 \[ \frac {343}{135 (2+3 x)^5}+\frac {1421}{108 (2+3 x)^4}+\frac {7189}{81 (2+3 x)^3}+\frac {1331}{2 (2+3 x)^2}+\frac {6655}{2+3 x}-33275 \log (2+3 x)+33275 \log (3+5 x) \]
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Rubi [A]
time = 0.02, antiderivative size = 70, 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 {6655}{3 x+2}+\frac {1331}{2 (3 x+2)^2}+\frac {7189}{81 (3 x+2)^3}+\frac {1421}{108 (3 x+2)^4}+\frac {343}{135 (3 x+2)^5}-33275 \log (3 x+2)+33275 \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)^6 (3+5 x)} \, dx &=\int \left (-\frac {343}{9 (2+3 x)^6}-\frac {1421}{9 (2+3 x)^5}-\frac {7189}{9 (2+3 x)^4}-\frac {3993}{(2+3 x)^3}-\frac {19965}{(2+3 x)^2}-\frac {99825}{2+3 x}+\frac {166375}{3+5 x}\right ) \, dx\\ &=\frac {343}{135 (2+3 x)^5}+\frac {1421}{108 (2+3 x)^4}+\frac {7189}{81 (2+3 x)^3}+\frac {1331}{2 (2+3 x)^2}+\frac {6655}{2+3 x}-33275 \log (2+3 x)+33275 \log (3+5 x)\\ \end {align*}
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Mathematica [A]
time = 0.04, size = 50, normalized size = 0.71 \begin {gather*} \frac {181744346+1075586865 x+2388229560 x^2+2357826570 x^3+873269100 x^4}{1620 (2+3 x)^5}-33275 \log (5 (2+3 x))+33275 \log (3+5 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 63, normalized size = 0.90
method | result | size |
risch | \(\frac {539055 x^{4}+\frac {2910897}{2} x^{3}+\frac {13267942}{9} x^{2}+\frac {71705791}{108} x +\frac {90872173}{810}}{\left (2+3 x \right )^{5}}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(47\) |
norman | \(\frac {-\frac {354933}{2} x -\frac {4200045}{4} x^{2}-\frac {55941409}{24} x^{3}-\frac {272616519}{320} x^{5}-\frac {73622413}{32} x^{4}}{\left (2+3 x \right )^{5}}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(50\) |
default | \(\frac {343}{135 \left (2+3 x \right )^{5}}+\frac {1421}{108 \left (2+3 x \right )^{4}}+\frac {7189}{81 \left (2+3 x \right )^{3}}+\frac {1331}{2 \left (2+3 x \right )^{2}}+\frac {6655}{2+3 x}-33275 \ln \left (2+3 x \right )+33275 \ln \left (3+5 x \right )\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 66, normalized size = 0.94 \begin {gather*} \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + 33275 \, \log \left (5 \, x + 3\right ) - 33275 \, \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 = 0.45, size = 115, normalized size = 1.64 \begin {gather*} \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (5 \, x + 3\right ) - 53905500 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 1075586865 \, x + 181744346}{1620 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 63, normalized size = 0.90 \begin {gather*} - \frac {- 873269100 x^{4} - 2357826570 x^{3} - 2388229560 x^{2} - 1075586865 x - 181744346}{393660 x^{5} + 1312200 x^{4} + 1749600 x^{3} + 1166400 x^{2} + 388800 x + 51840} + 33275 \log {\left (x + \frac {3}{5} \right )} - 33275 \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 = 0.55, size = 48, normalized size = 0.69 \begin {gather*} \frac {873269100 \, x^{4} + 2357826570 \, x^{3} + 2388229560 \, x^{2} + 1075586865 \, x + 181744346}{1620 \, {\left (3 \, x + 2\right )}^{5}} + 33275 \, \log \left ({\left | 5 \, x + 3 \right |}\right ) - 33275 \, \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 = 0.05, size = 55, normalized size = 0.79 \begin {gather*} \frac {\frac {6655\,x^4}{3}+\frac {11979\,x^3}{2}+\frac {13267942\,x^2}{2187}+\frac {71705791\,x}{26244}+\frac {90872173}{196830}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}}-66550\,\mathrm {atanh}\left (30\,x+19\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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