Optimal. Leaf size=67 \[ -\frac {49 (2+3 x)^{10}}{7290}+\frac {763 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{8748}+\frac {8285 (2+3 x)^{13}}{9477}-\frac {1900 (2+3 x)^{14}}{5103}+\frac {100 (2+3 x)^{15}}{2187} \]
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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 {100 (3 x+2)^{15}}{2187}-\frac {1900 (3 x+2)^{14}}{5103}+\frac {8285 (3 x+2)^{13}}{9477}-\frac {4099 (3 x+2)^{12}}{8748}+\frac {763 (3 x+2)^{11}}{8019}-\frac {49 (3 x+2)^{10}}{7290} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^9 (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^9+\frac {763}{243} (2+3 x)^{10}-\frac {4099}{243} (2+3 x)^{11}+\frac {8285}{243} (2+3 x)^{12}-\frac {3800}{243} (2+3 x)^{13}+\frac {500}{243} (2+3 x)^{14}\right ) \, dx\\ &=-\frac {49 (2+3 x)^{10}}{7290}+\frac {763 (2+3 x)^{11}}{8019}-\frac {4099 (2+3 x)^{12}}{8748}+\frac {8285 (2+3 x)^{13}}{9477}-\frac {1900 (2+3 x)^{14}}{5103}+\frac {100 (2+3 x)^{15}}{2187}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 90, normalized size = 1.34 \begin {gather*} 13824 x+100224 x^2+400128 x^3+871936 x^4+\frac {2732864 x^5}{5}-\frac {7363312 x^6}{3}-\frac {55216512 x^7}{7}-9703638 x^8-180666 x^9+\frac {182657511 x^{10}}{10}+\frac {342976275 x^{11}}{11}+\frac {113029263 x^{12}}{4}+\frac {200077695 x^{13}}{13}+\frac {33461100 x^{14}}{7}+656100 x^{15} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.09, size = 75, normalized size = 1.12
method | result | size |
gosper | \(\frac {x \left (39405366000 x^{14}+287096238000 x^{13}+924358950900 x^{12}+1697134383945 x^{11}+1872650461500 x^{10}+1097041011066 x^{9}-10850799960 x^{8}-582800498280 x^{7}-473757672960 x^{6}-147413506240 x^{5}+32827162368 x^{4}+52368476160 x^{3}+24031687680 x^{2}+6019453440 x +830269440\right )}{60060}\) | \(74\) |
default | \(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\) | \(75\) |
norman | \(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\) | \(75\) |
risch | \(13824 x +100224 x^{2}+400128 x^{3}+871936 x^{4}+\frac {2732864}{5} x^{5}-\frac {7363312}{3} x^{6}-\frac {55216512}{7} x^{7}-9703638 x^{8}-180666 x^{9}+\frac {182657511}{10} x^{10}+\frac {342976275}{11} x^{11}+\frac {113029263}{4} x^{12}+\frac {200077695}{13} x^{13}+\frac {33461100}{7} x^{14}+656100 x^{15}\) | \(75\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 74, normalized size = 1.10 \begin {gather*} 656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 74, normalized size = 1.10 \begin {gather*} 656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 87, normalized size = 1.30 \begin {gather*} 656100 x^{15} + \frac {33461100 x^{14}}{7} + \frac {200077695 x^{13}}{13} + \frac {113029263 x^{12}}{4} + \frac {342976275 x^{11}}{11} + \frac {182657511 x^{10}}{10} - 180666 x^{9} - 9703638 x^{8} - \frac {55216512 x^{7}}{7} - \frac {7363312 x^{6}}{3} + \frac {2732864 x^{5}}{5} + 871936 x^{4} + 400128 x^{3} + 100224 x^{2} + 13824 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.96, size = 74, normalized size = 1.10 \begin {gather*} 656100 \, x^{15} + \frac {33461100}{7} \, x^{14} + \frac {200077695}{13} \, x^{13} + \frac {113029263}{4} \, x^{12} + \frac {342976275}{11} \, x^{11} + \frac {182657511}{10} \, x^{10} - 180666 \, x^{9} - 9703638 \, x^{8} - \frac {55216512}{7} \, x^{7} - \frac {7363312}{3} \, x^{6} + \frac {2732864}{5} \, x^{5} + 871936 \, x^{4} + 400128 \, x^{3} + 100224 \, x^{2} + 13824 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.12, size = 74, normalized size = 1.10 \begin {gather*} 656100\,x^{15}+\frac {33461100\,x^{14}}{7}+\frac {200077695\,x^{13}}{13}+\frac {113029263\,x^{12}}{4}+\frac {342976275\,x^{11}}{11}+\frac {182657511\,x^{10}}{10}-180666\,x^9-9703638\,x^8-\frac {55216512\,x^7}{7}-\frac {7363312\,x^6}{3}+\frac {2732864\,x^5}{5}+871936\,x^4+400128\,x^3+100224\,x^2+13824\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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