Optimal. Leaf size=58 \[ \frac {833293 x}{78125}+\frac {305569 x^2}{31250}-\frac {72841 x^3}{3125}-\frac {102159 x^4}{2500}+\frac {7803 x^5}{625}+\frac {1404 x^6}{25}+\frac {972 x^7}{35}+\frac {121 \log (3+5 x)}{390625} \]
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Rubi [A]
time = 0.02, antiderivative size = 58, 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 {972 x^7}{35}+\frac {1404 x^6}{25}+\frac {7803 x^5}{625}-\frac {102159 x^4}{2500}-\frac {72841 x^3}{3125}+\frac {305569 x^2}{31250}+\frac {833293 x}{78125}+\frac {121 \log (5 x+3)}{390625} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int \frac {(1-2 x)^2 (2+3 x)^5}{3+5 x} \, dx &=\int \left (\frac {833293}{78125}+\frac {305569 x}{15625}-\frac {218523 x^2}{3125}-\frac {102159 x^3}{625}+\frac {7803 x^4}{125}+\frac {8424 x^5}{25}+\frac {972 x^6}{5}+\frac {121}{78125 (3+5 x)}\right ) \, dx\\ &=\frac {833293 x}{78125}+\frac {305569 x^2}{31250}-\frac {72841 x^3}{3125}-\frac {102159 x^4}{2500}+\frac {7803 x^5}{625}+\frac {1404 x^6}{25}+\frac {972 x^7}{35}+\frac {121 \log (3+5 x)}{390625}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 47, normalized size = 0.81 \begin {gather*} \frac {124071027+583305100 x+534745750 x^2-1274717500 x^3-2234728125 x^4+682762500 x^5+3071250000 x^6+1518750000 x^7+16940 \log (3+5 x)}{54687500} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 43, normalized size = 0.74
method | result | size |
default | \(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
norman | \(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
risch | \(\frac {833293 x}{78125}+\frac {305569 x^{2}}{31250}-\frac {72841 x^{3}}{3125}-\frac {102159 x^{4}}{2500}+\frac {7803 x^{5}}{625}+\frac {1404 x^{6}}{25}+\frac {972 x^{7}}{35}+\frac {121 \ln \left (3+5 x \right )}{390625}\) | \(43\) |
meijerg | \(\frac {121 \ln \left (1+\frac {5 x}{3}\right )}{390625}+\frac {112 x}{5}+\frac {56 x \left (-5 x +6\right )}{25}-\frac {126 x \left (\frac {100}{9} x^{2}-10 x +12\right )}{25}+\frac {567 x \left (-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{1250}+\frac {35721 x \left (\frac {2500}{27} x^{4}-\frac {625}{9} x^{3}+\frac {500}{9} x^{2}-50 x +60\right )}{62500}-\frac {6561 x \left (-\frac {218750}{243} x^{5}+\frac {17500}{27} x^{4}-\frac {4375}{9} x^{3}+\frac {3500}{9} x^{2}-350 x +420\right )}{78125}+\frac {59049 x \left (\frac {625000}{243} x^{6}-\frac {437500}{243} x^{5}+\frac {35000}{27} x^{4}-\frac {8750}{9} x^{3}+\frac {7000}{9} x^{2}-700 x +840\right )}{5468750}\) | \(136\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 42, normalized size = 0.72 \begin {gather*} \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 42, normalized size = 0.72 \begin {gather*} \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left (5 \, x + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 54, normalized size = 0.93 \begin {gather*} \frac {972 x^{7}}{35} + \frac {1404 x^{6}}{25} + \frac {7803 x^{5}}{625} - \frac {102159 x^{4}}{2500} - \frac {72841 x^{3}}{3125} + \frac {305569 x^{2}}{31250} + \frac {833293 x}{78125} + \frac {121 \log {\left (5 x + 3 \right )}}{390625} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.24, size = 43, normalized size = 0.74 \begin {gather*} \frac {972}{35} \, x^{7} + \frac {1404}{25} \, x^{6} + \frac {7803}{625} \, x^{5} - \frac {102159}{2500} \, x^{4} - \frac {72841}{3125} \, x^{3} + \frac {305569}{31250} \, x^{2} + \frac {833293}{78125} \, x + \frac {121}{390625} \, \log \left ({\left | 5 \, x + 3 \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 40, normalized size = 0.69 \begin {gather*} \frac {833293\,x}{78125}+\frac {121\,\ln \left (x+\frac {3}{5}\right )}{390625}+\frac {305569\,x^2}{31250}-\frac {72841\,x^3}{3125}-\frac {102159\,x^4}{2500}+\frac {7803\,x^5}{625}+\frac {1404\,x^6}{25}+\frac {972\,x^7}{35} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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