Optimal. Leaf size=45 \[ -\frac {49}{729} (2+3 x)^9+\frac {91}{270} (2+3 x)^{10}-\frac {16}{99} (2+3 x)^{11}+\frac {5}{243} (2+3 x)^{12} \]
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Rubi [A]
time = 0.02, antiderivative size = 45, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.050, Rules used = {78}
\begin {gather*} \frac {5}{243} (3 x+2)^{12}-\frac {16}{99} (3 x+2)^{11}+\frac {91}{270} (3 x+2)^{10}-\frac {49}{729} (3 x+2)^9 \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^8 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^8+\frac {91}{9} (2+3 x)^9-\frac {16}{3} (2+3 x)^{10}+\frac {20}{27} (2+3 x)^{11}\right ) \, dx\\ &=-\frac {49}{729} (2+3 x)^9+\frac {91}{270} (2+3 x)^{10}-\frac {16}{99} (2+3 x)^{11}+\frac {5}{243} (2+3 x)^{12}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 67, normalized size = 1.49 \begin {gather*} 768 x+3712 x^2+\frac {24832 x^3}{3}+3200 x^4-\frac {134112 x^5}{5}-62160 x^6-39312 x^7+59616 x^8+144315 x^9+\frac {1307097 x^{10}}{10}+\frac {647352 x^{11}}{11}+10935 x^{12} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 60, normalized size = 1.33
method | result | size |
gosper | \(\frac {x \left (3608550 x^{11}+19420560 x^{10}+43134201 x^{9}+47623950 x^{8}+19673280 x^{7}-12972960 x^{6}-20512800 x^{5}-8851392 x^{4}+1056000 x^{3}+2731520 x^{2}+1224960 x +253440\right )}{330}\) | \(59\) |
default | \(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\) | \(60\) |
norman | \(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\) | \(60\) |
risch | \(10935 x^{12}+\frac {647352}{11} x^{11}+\frac {1307097}{10} x^{10}+144315 x^{9}+59616 x^{8}-39312 x^{7}-62160 x^{6}-\frac {134112}{5} x^{5}+3200 x^{4}+\frac {24832}{3} x^{3}+3712 x^{2}+768 x\) | \(60\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 59, normalized size = 1.31 \begin {gather*} 10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.96, size = 59, normalized size = 1.31 \begin {gather*} 10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 65, normalized size = 1.44 \begin {gather*} 10935 x^{12} + \frac {647352 x^{11}}{11} + \frac {1307097 x^{10}}{10} + 144315 x^{9} + 59616 x^{8} - 39312 x^{7} - 62160 x^{6} - \frac {134112 x^{5}}{5} + 3200 x^{4} + \frac {24832 x^{3}}{3} + 3712 x^{2} + 768 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.55, size = 59, normalized size = 1.31 \begin {gather*} 10935 \, x^{12} + \frac {647352}{11} \, x^{11} + \frac {1307097}{10} \, x^{10} + 144315 \, x^{9} + 59616 \, x^{8} - 39312 \, x^{7} - 62160 \, x^{6} - \frac {134112}{5} \, x^{5} + 3200 \, x^{4} + \frac {24832}{3} \, x^{3} + 3712 \, x^{2} + 768 \, 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 = 1.31 \begin {gather*} 10935\,x^{12}+\frac {647352\,x^{11}}{11}+\frac {1307097\,x^{10}}{10}+144315\,x^9+59616\,x^8-39312\,x^7-62160\,x^6-\frac {134112\,x^5}{5}+3200\,x^4+\frac {24832\,x^3}{3}+3712\,x^2+768\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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