Optimal. Leaf size=78 \[ -\frac {343 (2+3 x)^6}{13122}+\frac {259}{729} (2+3 x)^7-\frac {10073 (2+3 x)^8}{5832}+\frac {66193 (2+3 x)^9}{19683}-\frac {1439}{729} (2+3 x)^{10}+\frac {3700 (2+3 x)^{11}}{8019}-\frac {250 (2+3 x)^{12}}{6561} \]
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Rubi [A]
time = 0.02, antiderivative size = 78, 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 {250 (3 x+2)^{12}}{6561}+\frac {3700 (3 x+2)^{11}}{8019}-\frac {1439}{729} (3 x+2)^{10}+\frac {66193 (3 x+2)^9}{19683}-\frac {10073 (3 x+2)^8}{5832}+\frac {259}{729} (3 x+2)^7-\frac {343 (3 x+2)^6}{13122} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^5 (3+5 x)^3 \, dx &=\int \left (-\frac {343}{729} (2+3 x)^5+\frac {1813}{243} (2+3 x)^6-\frac {10073}{243} (2+3 x)^7+\frac {66193}{729} (2+3 x)^8-\frac {14390}{243} (2+3 x)^9+\frac {3700}{243} (2+3 x)^{10}-\frac {1000}{729} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {343 (2+3 x)^6}{13122}+\frac {259}{729} (2+3 x)^7-\frac {10073 (2+3 x)^8}{5832}+\frac {66193 (2+3 x)^9}{19683}-\frac {1439}{729} (2+3 x)^{10}+\frac {3700 (2+3 x)^{11}}{8019}-\frac {250 (2+3 x)^{12}}{6561}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 65, normalized size = 0.83 \begin {gather*} 864 x+2808 x^2+1536 x^3-11798 x^4-24882 x^5+\frac {10297 x^6}{2}+71107 x^7+\frac {565167 x^8}{8}-32867 x^9-111159 x^{10}-\frac {882900 x^{11}}{11}-20250 x^{12} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 60, normalized size = 0.77
method | result | size |
gosper | \(-\frac {x \left (1782000 x^{11}+7063200 x^{10}+9781992 x^{9}+2892296 x^{8}-6216837 x^{7}-6257416 x^{6}-453068 x^{5}+2189616 x^{4}+1038224 x^{3}-135168 x^{2}-247104 x -76032\right )}{88}\) | \(59\) |
default | \(-20250 x^{12}-\frac {882900}{11} x^{11}-111159 x^{10}-32867 x^{9}+\frac {565167}{8} x^{8}+71107 x^{7}+\frac {10297}{2} x^{6}-24882 x^{5}-11798 x^{4}+1536 x^{3}+2808 x^{2}+864 x\) | \(60\) |
norman | \(-20250 x^{12}-\frac {882900}{11} x^{11}-111159 x^{10}-32867 x^{9}+\frac {565167}{8} x^{8}+71107 x^{7}+\frac {10297}{2} x^{6}-24882 x^{5}-11798 x^{4}+1536 x^{3}+2808 x^{2}+864 x\) | \(60\) |
risch | \(-20250 x^{12}-\frac {882900}{11} x^{11}-111159 x^{10}-32867 x^{9}+\frac {565167}{8} x^{8}+71107 x^{7}+\frac {10297}{2} x^{6}-24882 x^{5}-11798 x^{4}+1536 x^{3}+2808 x^{2}+864 x\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 59, normalized size = 0.76 \begin {gather*} -20250 \, x^{12} - \frac {882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac {565167}{8} \, x^{8} + 71107 \, x^{7} + \frac {10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 59, normalized size = 0.76 \begin {gather*} -20250 \, x^{12} - \frac {882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac {565167}{8} \, x^{8} + 71107 \, x^{7} + \frac {10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 63, normalized size = 0.81 \begin {gather*} - 20250 x^{12} - \frac {882900 x^{11}}{11} - 111159 x^{10} - 32867 x^{9} + \frac {565167 x^{8}}{8} + 71107 x^{7} + \frac {10297 x^{6}}{2} - 24882 x^{5} - 11798 x^{4} + 1536 x^{3} + 2808 x^{2} + 864 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.93, size = 59, normalized size = 0.76 \begin {gather*} -20250 \, x^{12} - \frac {882900}{11} \, x^{11} - 111159 \, x^{10} - 32867 \, x^{9} + \frac {565167}{8} \, x^{8} + 71107 \, x^{7} + \frac {10297}{2} \, x^{6} - 24882 \, x^{5} - 11798 \, x^{4} + 1536 \, x^{3} + 2808 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.07, size = 59, normalized size = 0.76 \begin {gather*} -20250\,x^{12}-\frac {882900\,x^{11}}{11}-111159\,x^{10}-32867\,x^9+\frac {565167\,x^8}{8}+71107\,x^7+\frac {10297\,x^6}{2}-24882\,x^5-11798\,x^4+1536\,x^3+2808\,x^2+864\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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