Optimal. Leaf size=67 \[ \frac {343 (2+3 x)^5}{3645}-\frac {1862 (2+3 x)^6}{2187}+\frac {1657}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{2916}+\frac {2180 (2+3 x)^9}{6561}-\frac {20}{729} (2+3 x)^{10} \]
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Rubi [A]
time = 0.02, antiderivative size = 67, 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 {20}{729} (3 x+2)^{10}+\frac {2180 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{2916}+\frac {1657}{729} (3 x+2)^7-\frac {1862 (3 x+2)^6}{2187}+\frac {343 (3 x+2)^5}{3645} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^3 (2+3 x)^4 (3+5 x)^2 \, dx &=\int \left (\frac {343}{243} (2+3 x)^4-\frac {3724}{243} (2+3 x)^5+\frac {11599}{243} (2+3 x)^6-\frac {8198}{243} (2+3 x)^7+\frac {2180}{243} (2+3 x)^8-\frac {200}{243} (2+3 x)^9\right ) \, dx\\ &=\frac {343 (2+3 x)^5}{3645}-\frac {1862 (2+3 x)^6}{2187}+\frac {1657}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{2916}+\frac {2180 (2+3 x)^9}{6561}-\frac {20}{729} (2+3 x)^{10}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 57, normalized size = 0.85 \begin {gather*} 144 x+240 x^2-\frac {1112 x^3}{3}-1386 x^4-\frac {399 x^5}{5}+\frac {10136 x^6}{3}+2823 x^7-\frac {9531 x^8}{4}-4260 x^9-1620 x^{10} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 50, normalized size = 0.75
method | result | size |
gosper | \(-\frac {x \left (97200 x^{9}+255600 x^{8}+142965 x^{7}-169380 x^{6}-202720 x^{5}+4788 x^{4}+83160 x^{3}+22240 x^{2}-14400 x -8640\right )}{60}\) | \(49\) |
default | \(-1620 x^{10}-4260 x^{9}-\frac {9531}{4} x^{8}+2823 x^{7}+\frac {10136}{3} x^{6}-\frac {399}{5} x^{5}-1386 x^{4}-\frac {1112}{3} x^{3}+240 x^{2}+144 x\) | \(50\) |
norman | \(-1620 x^{10}-4260 x^{9}-\frac {9531}{4} x^{8}+2823 x^{7}+\frac {10136}{3} x^{6}-\frac {399}{5} x^{5}-1386 x^{4}-\frac {1112}{3} x^{3}+240 x^{2}+144 x\) | \(50\) |
risch | \(-1620 x^{10}-4260 x^{9}-\frac {9531}{4} x^{8}+2823 x^{7}+\frac {10136}{3} x^{6}-\frac {399}{5} x^{5}-1386 x^{4}-\frac {1112}{3} x^{3}+240 x^{2}+144 x\) | \(50\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 49, normalized size = 0.73 \begin {gather*} -1620 \, x^{10} - 4260 \, x^{9} - \frac {9531}{4} \, x^{8} + 2823 \, x^{7} + \frac {10136}{3} \, x^{6} - \frac {399}{5} \, x^{5} - 1386 \, x^{4} - \frac {1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 49, normalized size = 0.73 \begin {gather*} -1620 \, x^{10} - 4260 \, x^{9} - \frac {9531}{4} \, x^{8} + 2823 \, x^{7} + \frac {10136}{3} \, x^{6} - \frac {399}{5} \, x^{5} - 1386 \, x^{4} - \frac {1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 54, normalized size = 0.81 \begin {gather*} - 1620 x^{10} - 4260 x^{9} - \frac {9531 x^{8}}{4} + 2823 x^{7} + \frac {10136 x^{6}}{3} - \frac {399 x^{5}}{5} - 1386 x^{4} - \frac {1112 x^{3}}{3} + 240 x^{2} + 144 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.38, size = 49, normalized size = 0.73 \begin {gather*} -1620 \, x^{10} - 4260 \, x^{9} - \frac {9531}{4} \, x^{8} + 2823 \, x^{7} + \frac {10136}{3} \, x^{6} - \frac {399}{5} \, x^{5} - 1386 \, x^{4} - \frac {1112}{3} \, x^{3} + 240 \, x^{2} + 144 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 49, normalized size = 0.73 \begin {gather*} -1620\,x^{10}-4260\,x^9-\frac {9531\,x^8}{4}+2823\,x^7+\frac {10136\,x^6}{3}-\frac {399\,x^5}{5}-1386\,x^4-\frac {1112\,x^3}{3}+240\,x^2+144\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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