Optimal. Leaf size=66 \[ 72 x+138 x^2+\frac {914 x^3}{3}+\frac {1615 x^4}{4}+\frac {2693 x^5}{5}+449 x^6+444 x^7+\frac {1863 x^8}{8}+\frac {1865 x^9}{9}+40 x^{10}+\frac {500 x^{11}}{11} \]
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Rubi [A]
time = 0.03, antiderivative size = 66, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {1671}
\begin {gather*} \frac {500 x^{11}}{11}+40 x^{10}+\frac {1865 x^9}{9}+\frac {1863 x^8}{8}+444 x^7+449 x^6+\frac {2693 x^5}{5}+\frac {1615 x^4}{4}+\frac {914 x^3}{3}+138 x^2+72 x \end {gather*}
Antiderivative was successfully verified.
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Rule 1671
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right )^2 \left (2+3 x+5 x^2\right )^3 \, dx &=\int \left (72+276 x+914 x^2+1615 x^3+2693 x^4+2694 x^5+3108 x^6+1863 x^7+1865 x^8+400 x^9+500 x^{10}\right ) \, dx\\ &=72 x+138 x^2+\frac {914 x^3}{3}+\frac {1615 x^4}{4}+\frac {2693 x^5}{5}+449 x^6+444 x^7+\frac {1863 x^8}{8}+\frac {1865 x^9}{9}+40 x^{10}+\frac {500 x^{11}}{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 66, normalized size = 1.00 \begin {gather*} 72 x+138 x^2+\frac {914 x^3}{3}+\frac {1615 x^4}{4}+\frac {2693 x^5}{5}+449 x^6+444 x^7+\frac {1863 x^8}{8}+\frac {1865 x^9}{9}+40 x^{10}+\frac {500 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 55, normalized size = 0.83
method | result | size |
gosper | \(72 x +138 x^{2}+\frac {914}{3} x^{3}+\frac {1615}{4} x^{4}+\frac {2693}{5} x^{5}+449 x^{6}+444 x^{7}+\frac {1863}{8} x^{8}+\frac {1865}{9} x^{9}+40 x^{10}+\frac {500}{11} x^{11}\) | \(55\) |
default | \(72 x +138 x^{2}+\frac {914}{3} x^{3}+\frac {1615}{4} x^{4}+\frac {2693}{5} x^{5}+449 x^{6}+444 x^{7}+\frac {1863}{8} x^{8}+\frac {1865}{9} x^{9}+40 x^{10}+\frac {500}{11} x^{11}\) | \(55\) |
norman | \(72 x +138 x^{2}+\frac {914}{3} x^{3}+\frac {1615}{4} x^{4}+\frac {2693}{5} x^{5}+449 x^{6}+444 x^{7}+\frac {1863}{8} x^{8}+\frac {1865}{9} x^{9}+40 x^{10}+\frac {500}{11} x^{11}\) | \(55\) |
risch | \(72 x +138 x^{2}+\frac {914}{3} x^{3}+\frac {1615}{4} x^{4}+\frac {2693}{5} x^{5}+449 x^{6}+444 x^{7}+\frac {1863}{8} x^{8}+\frac {1865}{9} x^{9}+40 x^{10}+\frac {500}{11} x^{11}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 54, normalized size = 0.82 \begin {gather*} \frac {500}{11} \, x^{11} + 40 \, x^{10} + \frac {1865}{9} \, x^{9} + \frac {1863}{8} \, x^{8} + 444 \, x^{7} + 449 \, x^{6} + \frac {2693}{5} \, x^{5} + \frac {1615}{4} \, x^{4} + \frac {914}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.49, size = 54, normalized size = 0.82 \begin {gather*} \frac {500}{11} \, x^{11} + 40 \, x^{10} + \frac {1865}{9} \, x^{9} + \frac {1863}{8} \, x^{8} + 444 \, x^{7} + 449 \, x^{6} + \frac {2693}{5} \, x^{5} + \frac {1615}{4} \, x^{4} + \frac {914}{3} \, x^{3} + 138 \, x^{2} + 72 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 63, normalized size = 0.95 \begin {gather*} \frac {500 x^{11}}{11} + 40 x^{10} + \frac {1865 x^{9}}{9} + \frac {1863 x^{8}}{8} + 444 x^{7} + 449 x^{6} + \frac {2693 x^{5}}{5} + \frac {1615 x^{4}}{4} + \frac {914 x^{3}}{3} + 138 x^{2} + 72 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.99, size = 54, normalized size = 0.82 \begin {gather*} \frac {500}{11} \, x^{11} + 40 \, x^{10} + \frac {1865}{9} \, x^{9} + \frac {1863}{8} \, x^{8} + 444 \, x^{7} + 449 \, x^{6} + \frac {2693}{5} \, x^{5} + \frac {1615}{4} \, x^{4} + \frac {914}{3} \, x^{3} + 138 \, x^{2} + 72 \, 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 = 0.82 \begin {gather*} \frac {500\,x^{11}}{11}+40\,x^{10}+\frac {1865\,x^9}{9}+\frac {1863\,x^8}{8}+444\,x^7+449\,x^6+\frac {2693\,x^5}{5}+\frac {1615\,x^4}{4}+\frac {914\,x^3}{3}+138\,x^2+72\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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