Optimal. Leaf size=45 \[ -\frac {49}{405} (2+3 x)^5+\frac {91}{162} (2+3 x)^6-\frac {16}{63} (2+3 x)^7+\frac {5}{162} (2+3 x)^8 \]
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Rubi [A]
time = 0.01, 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}{162} (3 x+2)^8-\frac {16}{63} (3 x+2)^7+\frac {91}{162} (3 x+2)^6-\frac {49}{405} (3 x+2)^5 \end {gather*}
Antiderivative was successfully verified.
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Rule 78
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x) \, dx &=\int \left (-\frac {49}{27} (2+3 x)^4+\frac {91}{9} (2+3 x)^5-\frac {16}{3} (2+3 x)^6+\frac {20}{27} (2+3 x)^7\right ) \, dx\\ &=-\frac {49}{405} (2+3 x)^5+\frac {91}{162} (2+3 x)^6-\frac {16}{63} (2+3 x)^7+\frac {5}{162} (2+3 x)^8\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 49, normalized size = 1.09 \begin {gather*} 48 x+88 x^2-\frac {152 x^3}{3}-328 x^4-\frac {1077 x^5}{5}+\frac {675 x^6}{2}+\frac {3672 x^7}{7}+\frac {405 x^8}{2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 40, normalized size = 0.89
method | result | size |
gosper | \(\frac {x \left (42525 x^{7}+110160 x^{6}+70875 x^{5}-45234 x^{4}-68880 x^{3}-10640 x^{2}+18480 x +10080\right )}{210}\) | \(39\) |
default | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
norman | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
risch | \(\frac {405}{2} x^{8}+\frac {3672}{7} x^{7}+\frac {675}{2} x^{6}-\frac {1077}{5} x^{5}-328 x^{4}-\frac {152}{3} x^{3}+88 x^{2}+48 x\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 39, normalized size = 0.87 \begin {gather*} \frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.73, size = 39, normalized size = 0.87 \begin {gather*} \frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 46, normalized size = 1.02 \begin {gather*} \frac {405 x^{8}}{2} + \frac {3672 x^{7}}{7} + \frac {675 x^{6}}{2} - \frac {1077 x^{5}}{5} - 328 x^{4} - \frac {152 x^{3}}{3} + 88 x^{2} + 48 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.71, size = 39, normalized size = 0.87 \begin {gather*} \frac {405}{2} \, x^{8} + \frac {3672}{7} \, x^{7} + \frac {675}{2} \, x^{6} - \frac {1077}{5} \, x^{5} - 328 \, x^{4} - \frac {152}{3} \, x^{3} + 88 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 39, normalized size = 0.87 \begin {gather*} \frac {405\,x^8}{2}+\frac {3672\,x^7}{7}+\frac {675\,x^6}{2}-\frac {1077\,x^5}{5}-328\,x^4-\frac {152\,x^3}{3}+88\,x^2+48\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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