Optimal. Leaf size=67 \[ \frac {500 (3 x+2)^{13}}{9477}-\frac {950 (3 x+2)^{12}}{2187}+\frac {8285 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{7290}+\frac {763 (3 x+2)^9}{6561}-\frac {49 (3 x+2)^8}{5832} \]
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Rubi [A] time = 0.03, 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 = {88} \begin {gather*} \frac {500 (3 x+2)^{13}}{9477}-\frac {950 (3 x+2)^{12}}{2187}+\frac {8285 (3 x+2)^{11}}{8019}-\frac {4099 (3 x+2)^{10}}{7290}+\frac {763 (3 x+2)^9}{6561}-\frac {49 (3 x+2)^8}{5832} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^7+\frac {763}{243} (2+3 x)^8-\frac {4099}{243} (2+3 x)^9+\frac {8285}{243} (2+3 x)^{10}-\frac {3800}{243} (2+3 x)^{11}+\frac {500}{243} (2+3 x)^{12}\right ) \, dx\\ &=-\frac {49 (2+3 x)^8}{5832}+\frac {763 (2+3 x)^9}{6561}-\frac {4099 (2+3 x)^{10}}{7290}+\frac {8285 (2+3 x)^{11}}{8019}-\frac {950 (2+3 x)^{12}}{2187}+\frac {500 (2+3 x)^{13}}{9477}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 76, normalized size = 1.13 \begin {gather*} \frac {1093500 x^{13}}{13}+498150 x^{12}+\frac {13774455 x^{11}}{11}+\frac {16653681 x^{10}}{10}+1086843 x^9-\frac {148473 x^8}{8}-618582 x^7-\frac {1393018 x^6}{3}-\frac {495976 x^5}{5}+65812 x^4+57696 x^3+19872 x^2+3456 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int (1-2 x)^2 (2+3 x)^7 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 1.33, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} x^{13} + 498150 x^{12} + \frac {13774455}{11} x^{11} + \frac {16653681}{10} x^{10} + 1086843 x^{9} - \frac {148473}{8} x^{8} - 618582 x^{7} - \frac {1393018}{3} x^{6} - \frac {495976}{5} x^{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.90, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 65, normalized size = 0.97 \begin {gather*} \frac {1093500}{13} x^{13}+498150 x^{12}+\frac {13774455}{11} x^{11}+\frac {16653681}{10} x^{10}+1086843 x^{9}-\frac {148473}{8} x^{8}-618582 x^{7}-\frac {1393018}{3} x^{6}-\frac {495976}{5} x^{5}+65812 x^{4}+57696 x^{3}+19872 x^{2}+3456 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500}{13} \, x^{13} + 498150 \, x^{12} + \frac {13774455}{11} \, x^{11} + \frac {16653681}{10} \, x^{10} + 1086843 \, x^{9} - \frac {148473}{8} \, x^{8} - 618582 \, x^{7} - \frac {1393018}{3} \, x^{6} - \frac {495976}{5} \, x^{5} + 65812 \, x^{4} + 57696 \, x^{3} + 19872 \, x^{2} + 3456 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 64, normalized size = 0.96 \begin {gather*} \frac {1093500\,x^{13}}{13}+498150\,x^{12}+\frac {13774455\,x^{11}}{11}+\frac {16653681\,x^{10}}{10}+1086843\,x^9-\frac {148473\,x^8}{8}-618582\,x^7-\frac {1393018\,x^6}{3}-\frac {495976\,x^5}{5}+65812\,x^4+57696\,x^3+19872\,x^2+3456\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 73, normalized size = 1.09 \begin {gather*} \frac {1093500 x^{13}}{13} + 498150 x^{12} + \frac {13774455 x^{11}}{11} + \frac {16653681 x^{10}}{10} + 1086843 x^{9} - \frac {148473 x^{8}}{8} - 618582 x^{7} - \frac {1393018 x^{6}}{3} - \frac {495976 x^{5}}{5} + 65812 x^{4} + 57696 x^{3} + 19872 x^{2} + 3456 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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