Optimal. Leaf size=76 \[ \frac {1}{945 (2+3 x)^5}-\frac {103}{5292 (2+3 x)^4}+\frac {3469}{27783 (2+3 x)^3}-\frac {1331}{4802 (2+3 x)^2}-\frac {2662}{16807 (2+3 x)}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (2+3 x)}{117649} \]
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Rubi [A]
time = 0.02, antiderivative size = 76, 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 {2662}{16807 (3 x+2)}-\frac {1331}{4802 (3 x+2)^2}+\frac {3469}{27783 (3 x+2)^3}-\frac {103}{5292 (3 x+2)^4}+\frac {1}{945 (3 x+2)^5}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (3 x+2)}{117649} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(3+5 x)^3}{(1-2 x) (2+3 x)^6} \, dx &=\int \left (-\frac {10648}{117649 (-1+2 x)}-\frac {1}{63 (2+3 x)^6}+\frac {103}{441 (2+3 x)^5}-\frac {3469}{3087 (2+3 x)^4}+\frac {3993}{2401 (2+3 x)^3}+\frac {7986}{16807 (2+3 x)^2}+\frac {15972}{117649 (2+3 x)}\right ) \, dx\\ &=\frac {1}{945 (2+3 x)^5}-\frac {103}{5292 (2+3 x)^4}+\frac {3469}{27783 (2+3 x)^3}-\frac {1331}{4802 (2+3 x)^2}-\frac {2662}{16807 (2+3 x)}-\frac {5324 \log (1-2 x)}{117649}+\frac {5324 \log (2+3 x)}{117649}\\ \end {align*}
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Mathematica [A]
time = 0.05, size = 52, normalized size = 0.68 \begin {gather*} \frac {2 \left (-\frac {7 \left (116805778+646472325 x+1308416040 x^2+1135249830 x^3+349307640 x^4\right )}{8 (2+3 x)^5}-1078110 \log (1-2 x)+1078110 \log (4+6 x)\right )}{47647845} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 63, normalized size = 0.83
method | result | size |
risch | \(\frac {-\frac {215622}{16807} x^{4}-\frac {1401543}{33614} x^{3}-\frac {7268978}{151263} x^{2}-\frac {43098155}{1815156} x -\frac {58402889}{13613670}}{\left (2+3 x \right )^{5}}-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(47\) |
norman | \(\frac {\frac {283421}{33614} x +\frac {3258553}{67228} x^{2}+\frac {41584373}{403368} x^{3}+\frac {175208667}{5378240} x^{5}+\frac {51502985}{537824} x^{4}}{\left (2+3 x \right )^{5}}-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(50\) |
default | \(-\frac {5324 \ln \left (-1+2 x \right )}{117649}+\frac {1}{945 \left (2+3 x \right )^{5}}-\frac {103}{5292 \left (2+3 x \right )^{4}}+\frac {3469}{27783 \left (2+3 x \right )^{3}}-\frac {1331}{4802 \left (2+3 x \right )^{2}}-\frac {2662}{16807 \left (2+3 x \right )}+\frac {5324 \ln \left (2+3 x \right )}{117649}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 66, normalized size = 0.87 \begin {gather*} -\frac {349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )}} + \frac {5324}{117649} \, \log \left (3 \, x + 2\right ) - \frac {5324}{117649} \, \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 = 0.45, size = 115, normalized size = 1.51 \begin {gather*} -\frac {2445153480 \, x^{4} + 7946748810 \, x^{3} + 9158912280 \, x^{2} - 8624880 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (3 \, x + 2\right ) + 8624880 \, {\left (243 \, x^{5} + 810 \, x^{4} + 1080 \, x^{3} + 720 \, x^{2} + 240 \, x + 32\right )} \log \left (2 \, x - 1\right ) + 4525306275 \, x + 817640446}{190591380 \, {\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 = 0.08, size = 65, normalized size = 0.86 \begin {gather*} - \frac {349307640 x^{4} + 1135249830 x^{3} + 1308416040 x^{2} + 646472325 x + 116805778}{6616243620 x^{5} + 22054145400 x^{4} + 29405527200 x^{3} + 19603684800 x^{2} + 6534561600 x + 871274880} - \frac {5324 \log {\left (x - \frac {1}{2} \right )}}{117649} + \frac {5324 \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 = 0.96, size = 48, normalized size = 0.63 \begin {gather*} -\frac {349307640 \, x^{4} + 1135249830 \, x^{3} + 1308416040 \, x^{2} + 646472325 \, x + 116805778}{27227340 \, {\left (3 \, x + 2\right )}^{5}} + \frac {5324}{117649} \, \log \left ({\left | 3 \, x + 2 \right |}\right ) - \frac {5324}{117649} \, \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 = 0.04, size = 56, normalized size = 0.74 \begin {gather*} \frac {10648\,\mathrm {atanh}\left (\frac {12\,x}{7}+\frac {1}{7}\right )}{117649}-\frac {\frac {2662\,x^4}{50421}+\frac {17303\,x^3}{100842}+\frac {7268978\,x^2}{36756909}+\frac {43098155\,x}{441082908}+\frac {58402889}{3308121810}}{x^5+\frac {10\,x^4}{3}+\frac {40\,x^3}{9}+\frac {80\,x^2}{27}+\frac {80\,x}{81}+\frac {32}{243}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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