Optimal. Leaf size=67 \[ \frac {50}{729} (3 x+2)^{10}-\frac {3800 (3 x+2)^9}{6561}+\frac {8285 (3 x+2)^8}{5832}-\frac {4099 (3 x+2)^7}{5103}+\frac {763 (3 x+2)^6}{4374}-\frac {49 (3 x+2)^5}{3645} \]
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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} \[ \frac {50}{729} (3 x+2)^{10}-\frac {3800 (3 x+2)^9}{6561}+\frac {8285 (3 x+2)^8}{5832}-\frac {4099 (3 x+2)^7}{5103}+\frac {763 (3 x+2)^6}{4374}-\frac {49 (3 x+2)^5}{3645} \]
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^4 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^4+\frac {763}{243} (2+3 x)^5-\frac {4099}{243} (2+3 x)^6+\frac {8285}{243} (2+3 x)^7-\frac {3800}{243} (2+3 x)^8+\frac {500}{243} (2+3 x)^9\right ) \, dx\\ &=-\frac {49 (2+3 x)^5}{3645}+\frac {763 (2+3 x)^6}{4374}-\frac {4099 (2+3 x)^7}{5103}+\frac {8285 (2+3 x)^8}{5832}-\frac {3800 (2+3 x)^9}{6561}+\frac {50}{729} (2+3 x)^{10}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 57, normalized size = 0.85 \[ 4050 x^{10}+15600 x^9+\frac {175365 x^8}{8}+\frac {66873 x^7}{7}-\frac {46885 x^6}{6}-\frac {52853 x^5}{5}-2992 x^4+1704 x^3+1512 x^2+432 x \]
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 49, normalized size = 0.73 \[ 4050 x^{10} + 15600 x^{9} + \frac {175365}{8} x^{8} + \frac {66873}{7} x^{7} - \frac {46885}{6} x^{6} - \frac {52853}{5} x^{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 49, normalized size = 0.73 \[ 4050 \, x^{10} + 15600 \, x^{9} + \frac {175365}{8} \, x^{8} + \frac {66873}{7} \, x^{7} - \frac {46885}{6} \, x^{6} - \frac {52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 50, normalized size = 0.75 \[ 4050 x^{10}+15600 x^{9}+\frac {175365}{8} x^{8}+\frac {66873}{7} x^{7}-\frac {46885}{6} x^{6}-\frac {52853}{5} x^{5}-2992 x^{4}+1704 x^{3}+1512 x^{2}+432 x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 49, normalized size = 0.73 \[ 4050 \, x^{10} + 15600 \, x^{9} + \frac {175365}{8} \, x^{8} + \frac {66873}{7} \, x^{7} - \frac {46885}{6} \, x^{6} - \frac {52853}{5} \, x^{5} - 2992 \, x^{4} + 1704 \, x^{3} + 1512 \, x^{2} + 432 \, x \]
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 \[ 4050\,x^{10}+15600\,x^9+\frac {175365\,x^8}{8}+\frac {66873\,x^7}{7}-\frac {46885\,x^6}{6}-\frac {52853\,x^5}{5}-2992\,x^4+1704\,x^3+1512\,x^2+432\,x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 54, normalized size = 0.81 \[ 4050 x^{10} + 15600 x^{9} + \frac {175365 x^{8}}{8} + \frac {66873 x^{7}}{7} - \frac {46885 x^{6}}{6} - \frac {52853 x^{5}}{5} - 2992 x^{4} + 1704 x^{3} + 1512 x^{2} + 432 x \]
Verification of antiderivative is not currently implemented for this CAS.
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