Optimal. Leaf size=67 \[ -\frac {49 (2+3 x)^{11}}{8019}+\frac {763 (2+3 x)^{12}}{8748}-\frac {4099 (2+3 x)^{13}}{9477}+\frac {8285 (2+3 x)^{14}}{10206}-\frac {760 (2+3 x)^{15}}{2187}+\frac {125 (2+3 x)^{16}}{2916} \]
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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 {125 (3 x+2)^{16}}{2916}-\frac {760 (3 x+2)^{15}}{2187}+\frac {8285 (3 x+2)^{14}}{10206}-\frac {4099 (3 x+2)^{13}}{9477}+\frac {763 (3 x+2)^{12}}{8748}-\frac {49 (3 x+2)^{11}}{8019} \end {gather*}
Antiderivative was successfully verified.
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Rule 90
Rubi steps
\begin {align*} \int (1-2 x)^2 (2+3 x)^{10} (3+5 x)^3 \, dx &=\int \left (-\frac {49}{243} (2+3 x)^{10}+\frac {763}{243} (2+3 x)^{11}-\frac {4099}{243} (2+3 x)^{12}+\frac {8285}{243} (2+3 x)^{13}-\frac {3800}{243} (2+3 x)^{14}+\frac {500}{243} (2+3 x)^{15}\right ) \, dx\\ &=-\frac {49 (2+3 x)^{11}}{8019}+\frac {763 (2+3 x)^{12}}{8748}-\frac {4099 (2+3 x)^{13}}{9477}+\frac {8285 (2+3 x)^{14}}{10206}-\frac {760 (2+3 x)^{15}}{2187}+\frac {125 (2+3 x)^{16}}{2916}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 93, normalized size = 1.39 \begin {gather*} 27648 x+221184 x^2+1000704 x^3+2644160 x^4+3185792 x^5-\frac {10627328 x^6}{3}-\frac {154612896 x^7}{7}-40113468 x^8-26237700 x^9+36043704 x^{10}+\frac {1233925083 x^{11}}{11}+\frac {569034801 x^{12}}{4}+\frac {1417418757 x^{13}}{13}+\frac {734077485 x^{14}}{14}+14696640 x^{15}+\frac {7381125 x^{16}}{4} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.08, size = 80, normalized size = 1.19
method | result | size |
gosper | \(\frac {x \left (22165518375 x^{15}+176536039680 x^{14}+629838482130 x^{13}+1309694931468 x^{12}+1708811507403 x^{11}+1347446190636 x^{10}+432956972448 x^{9}-315167252400 x^{8}-481842977616 x^{7}-265315729536 x^{6}-42551821312 x^{5}+38267733504 x^{4}+31761649920 x^{3}+12020456448 x^{2}+2656862208 x +332107776\right )}{12012}\) | \(79\) |
default | \(27648 x +221184 x^{2}+1000704 x^{3}+2644160 x^{4}+3185792 x^{5}-\frac {10627328}{3} x^{6}-\frac {154612896}{7} x^{7}-40113468 x^{8}-26237700 x^{9}+36043704 x^{10}+\frac {1233925083}{11} x^{11}+\frac {569034801}{4} x^{12}+\frac {1417418757}{13} x^{13}+\frac {734077485}{14} x^{14}+14696640 x^{15}+\frac {7381125}{4} x^{16}\) | \(80\) |
norman | \(27648 x +221184 x^{2}+1000704 x^{3}+2644160 x^{4}+3185792 x^{5}-\frac {10627328}{3} x^{6}-\frac {154612896}{7} x^{7}-40113468 x^{8}-26237700 x^{9}+36043704 x^{10}+\frac {1233925083}{11} x^{11}+\frac {569034801}{4} x^{12}+\frac {1417418757}{13} x^{13}+\frac {734077485}{14} x^{14}+14696640 x^{15}+\frac {7381125}{4} x^{16}\) | \(80\) |
risch | \(27648 x +221184 x^{2}+1000704 x^{3}+2644160 x^{4}+3185792 x^{5}-\frac {10627328}{3} x^{6}-\frac {154612896}{7} x^{7}-40113468 x^{8}-26237700 x^{9}+36043704 x^{10}+\frac {1233925083}{11} x^{11}+\frac {569034801}{4} x^{12}+\frac {1417418757}{13} x^{13}+\frac {734077485}{14} x^{14}+14696640 x^{15}+\frac {7381125}{4} x^{16}\) | \(80\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.32, size = 79, normalized size = 1.18 \begin {gather*} \frac {7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac {734077485}{14} \, x^{14} + \frac {1417418757}{13} \, x^{13} + \frac {569034801}{4} \, x^{12} + \frac {1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac {154612896}{7} \, x^{7} - \frac {10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 79, normalized size = 1.18 \begin {gather*} \frac {7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac {734077485}{14} \, x^{14} + \frac {1417418757}{13} \, x^{13} + \frac {569034801}{4} \, x^{12} + \frac {1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac {154612896}{7} \, x^{7} - \frac {10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 90, normalized size = 1.34 \begin {gather*} \frac {7381125 x^{16}}{4} + 14696640 x^{15} + \frac {734077485 x^{14}}{14} + \frac {1417418757 x^{13}}{13} + \frac {569034801 x^{12}}{4} + \frac {1233925083 x^{11}}{11} + 36043704 x^{10} - 26237700 x^{9} - 40113468 x^{8} - \frac {154612896 x^{7}}{7} - \frac {10627328 x^{6}}{3} + 3185792 x^{5} + 2644160 x^{4} + 1000704 x^{3} + 221184 x^{2} + 27648 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.68, size = 79, normalized size = 1.18 \begin {gather*} \frac {7381125}{4} \, x^{16} + 14696640 \, x^{15} + \frac {734077485}{14} \, x^{14} + \frac {1417418757}{13} \, x^{13} + \frac {569034801}{4} \, x^{12} + \frac {1233925083}{11} \, x^{11} + 36043704 \, x^{10} - 26237700 \, x^{9} - 40113468 \, x^{8} - \frac {154612896}{7} \, x^{7} - \frac {10627328}{3} \, x^{6} + 3185792 \, x^{5} + 2644160 \, x^{4} + 1000704 \, x^{3} + 221184 \, x^{2} + 27648 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.15, size = 79, normalized size = 1.18 \begin {gather*} \frac {7381125\,x^{16}}{4}+14696640\,x^{15}+\frac {734077485\,x^{14}}{14}+\frac {1417418757\,x^{13}}{13}+\frac {569034801\,x^{12}}{4}+\frac {1233925083\,x^{11}}{11}+36043704\,x^{10}-26237700\,x^9-40113468\,x^8-\frac {154612896\,x^7}{7}-\frac {10627328\,x^6}{3}+3185792\,x^5+2644160\,x^4+1000704\,x^3+221184\,x^2+27648\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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