Optimal. Leaf size=67 \[ \frac {343 (2+3 x)^6}{4374}-\frac {532}{729} (2+3 x)^7+\frac {11599 (2+3 x)^8}{5832}-\frac {8198 (2+3 x)^9}{6561}+\frac {218}{729} (2+3 x)^{10}-\frac {200 (2+3 x)^{11}}{8019} \]
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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 {200 (3 x+2)^{11}}{8019}+\frac {218}{729} (3 x+2)^{10}-\frac {8198 (3 x+2)^9}{6561}+\frac {11599 (3 x+2)^8}{5832}-\frac {532}{729} (3 x+2)^7+\frac {343 (3 x+2)^6}{4374} \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)^2 \, dx &=\int \left (\frac {343}{243} (2+3 x)^5-\frac {3724}{243} (2+3 x)^6+\frac {11599}{243} (2+3 x)^7-\frac {8198}{243} (2+3 x)^8+\frac {2180}{243} (2+3 x)^9-\frac {200}{243} (2+3 x)^{10}\right ) \, dx\\ &=\frac {343 (2+3 x)^6}{4374}-\frac {532}{729} (2+3 x)^7+\frac {11599 (2+3 x)^8}{5832}-\frac {8198 (2+3 x)^9}{6561}+\frac {218}{729} (2+3 x)^{10}-\frac {200 (2+3 x)^{11}}{8019}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 62, normalized size = 0.93 \begin {gather*} 288 x+696 x^2-\frac {784 x^3}{3}-3606 x^4-3486 x^5+\frac {39347 x^6}{6}+14334 x^7+\frac {21159 x^8}{8}-14874 x^9-14742 x^{10}-\frac {48600 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 55, normalized size = 0.82
method | result | size |
gosper | \(-\frac {x \left (1166400 x^{10}+3891888 x^{9}+3926736 x^{8}-698247 x^{7}-3784176 x^{6}-1731268 x^{5}+920304 x^{4}+951984 x^{3}+68992 x^{2}-183744 x -76032\right )}{264}\) | \(54\) |
default | \(-\frac {48600}{11} x^{11}-14742 x^{10}-14874 x^{9}+\frac {21159}{8} x^{8}+14334 x^{7}+\frac {39347}{6} x^{6}-3486 x^{5}-3606 x^{4}-\frac {784}{3} x^{3}+696 x^{2}+288 x\) | \(55\) |
norman | \(-\frac {48600}{11} x^{11}-14742 x^{10}-14874 x^{9}+\frac {21159}{8} x^{8}+14334 x^{7}+\frac {39347}{6} x^{6}-3486 x^{5}-3606 x^{4}-\frac {784}{3} x^{3}+696 x^{2}+288 x\) | \(55\) |
risch | \(-\frac {48600}{11} x^{11}-14742 x^{10}-14874 x^{9}+\frac {21159}{8} x^{8}+14334 x^{7}+\frac {39347}{6} x^{6}-3486 x^{5}-3606 x^{4}-\frac {784}{3} x^{3}+696 x^{2}+288 x\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 54, normalized size = 0.81 \begin {gather*} -\frac {48600}{11} \, x^{11} - 14742 \, x^{10} - 14874 \, x^{9} + \frac {21159}{8} \, x^{8} + 14334 \, x^{7} + \frac {39347}{6} \, x^{6} - 3486 \, x^{5} - 3606 \, x^{4} - \frac {784}{3} \, x^{3} + 696 \, x^{2} + 288 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 54, normalized size = 0.81 \begin {gather*} -\frac {48600}{11} \, x^{11} - 14742 \, x^{10} - 14874 \, x^{9} + \frac {21159}{8} \, x^{8} + 14334 \, x^{7} + \frac {39347}{6} \, x^{6} - 3486 \, x^{5} - 3606 \, x^{4} - \frac {784}{3} \, x^{3} + 696 \, x^{2} + 288 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 60, normalized size = 0.90 \begin {gather*} - \frac {48600 x^{11}}{11} - 14742 x^{10} - 14874 x^{9} + \frac {21159 x^{8}}{8} + 14334 x^{7} + \frac {39347 x^{6}}{6} - 3486 x^{5} - 3606 x^{4} - \frac {784 x^{3}}{3} + 696 x^{2} + 288 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.76, size = 54, normalized size = 0.81 \begin {gather*} -\frac {48600}{11} \, x^{11} - 14742 \, x^{10} - 14874 \, x^{9} + \frac {21159}{8} \, x^{8} + 14334 \, x^{7} + \frac {39347}{6} \, x^{6} - 3486 \, x^{5} - 3606 \, x^{4} - \frac {784}{3} \, x^{3} + 696 \, x^{2} + 288 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.05, size = 54, normalized size = 0.81 \begin {gather*} -\frac {48600\,x^{11}}{11}-14742\,x^{10}-14874\,x^9+\frac {21159\,x^8}{8}+14334\,x^7+\frac {39347\,x^6}{6}-3486\,x^5-3606\,x^4-\frac {784\,x^3}{3}+696\,x^2+288\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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