Optimal. Leaf size=67 \[ \frac {500 (3 x+2)^{11}}{8019}-\frac {380}{729} (3 x+2)^{10}+\frac {8285 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{5832}+\frac {109}{729} (3 x+2)^7-\frac {49 (3 x+2)^6}{4374} \]
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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)^{11}}{8019}-\frac {380}{729} (3 x+2)^{10}+\frac {8285 (3 x+2)^9}{6561}-\frac {4099 (3 x+2)^8}{5832}+\frac {109}{729} (3 x+2)^7-\frac {49 (3 x+2)^6}{4374} \end {gather*}
Antiderivative was successfully verified.
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Rule 88
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^5 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^5+\frac {763}{243} (2+3 x)^6-\frac {4099}{243} (2+3 x)^7+\frac {8285}{243} (2+3 x)^8-\frac {3800}{243} (2+3 x)^9+\frac {500}{243} (2+3 x)^{10}\right ) \, dx\\ &=-\frac {49 (2+3 x)^6}{4374}+\frac {109}{729} (2+3 x)^7-\frac {4099 (2+3 x)^8}{5832}+\frac {8285 (2+3 x)^9}{6561}-\frac {380}{729} (2+3 x)^{10}+\frac {500 (2+3 x)^{11}}{8019}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 60, normalized size = 0.90 \begin {gather*} \frac {121500 x^{11}}{11}+50220 x^{10}+89655 x^9+\frac {551349 x^8}{8}-987 x^7-\frac {252329 x^6}{6}-28322 x^5-2150 x^4+6432 x^3+3672 x^2+864 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)^5 (3+5 x)^3 \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.56, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} x^{11} + 50220 x^{10} + 89655 x^{9} + \frac {551349}{8} x^{8} - 987 x^{7} - \frac {252329}{6} x^{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.02, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 55, normalized size = 0.82 \begin {gather*} \frac {121500}{11} x^{11}+50220 x^{10}+89655 x^{9}+\frac {551349}{8} x^{8}-987 x^{7}-\frac {252329}{6} x^{6}-28322 x^{5}-2150 x^{4}+6432 x^{3}+3672 x^{2}+864 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.57, size = 54, normalized size = 0.81 \begin {gather*} \frac {121500}{11} \, x^{11} + 50220 \, x^{10} + 89655 \, x^{9} + \frac {551349}{8} \, x^{8} - 987 \, x^{7} - \frac {252329}{6} \, x^{6} - 28322 \, x^{5} - 2150 \, x^{4} + 6432 \, x^{3} + 3672 \, x^{2} + 864 \, 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 {121500\,x^{11}}{11}+50220\,x^{10}+89655\,x^9+\frac {551349\,x^8}{8}-987\,x^7-\frac {252329\,x^6}{6}-28322\,x^5-2150\,x^4+6432\,x^3+3672\,x^2+864\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 58, normalized size = 0.87 \begin {gather*} \frac {121500 x^{11}}{11} + 50220 x^{10} + 89655 x^{9} + \frac {551349 x^{8}}{8} - 987 x^{7} - \frac {252329 x^{6}}{6} - 28322 x^{5} - 2150 x^{4} + 6432 x^{3} + 3672 x^{2} + 864 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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