Optimal. Leaf size=68 \[ 48 x+136 x^2+\frac {1064 x^3}{3}+656 x^4+\frac {5099 x^5}{5}+\frac {2377 x^6}{2}+1176 x^7+\frac {3415 x^8}{4}+\frac {5075 x^9}{9}+\frac {475 x^{10}}{2}+\frac {1250 x^{11}}{11} \]
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Rubi [A]
time = 0.03, antiderivative size = 68, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {1671}
\begin {gather*} \frac {1250 x^{11}}{11}+\frac {475 x^{10}}{2}+\frac {5075 x^9}{9}+\frac {3415 x^8}{4}+1176 x^7+\frac {2377 x^6}{2}+\frac {5099 x^5}{5}+656 x^4+\frac {1064 x^3}{3}+136 x^2+48 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 ) \left (2+3 x+5 x^2\right )^4 \, dx &=\int \left (48+272 x+1064 x^2+2624 x^3+5099 x^4+7131 x^5+8232 x^6+6830 x^7+5075 x^8+2375 x^9+1250 x^{10}\right ) \, dx\\ &=48 x+136 x^2+\frac {1064 x^3}{3}+656 x^4+\frac {5099 x^5}{5}+\frac {2377 x^6}{2}+1176 x^7+\frac {3415 x^8}{4}+\frac {5075 x^9}{9}+\frac {475 x^{10}}{2}+\frac {1250 x^{11}}{11}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 68, normalized size = 1.00 \begin {gather*} 48 x+136 x^2+\frac {1064 x^3}{3}+656 x^4+\frac {5099 x^5}{5}+\frac {2377 x^6}{2}+1176 x^7+\frac {3415 x^8}{4}+\frac {5075 x^9}{9}+\frac {475 x^{10}}{2}+\frac {1250 x^{11}}{11} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 55, normalized size = 0.81
method | result | size |
gosper | \(48 x +136 x^{2}+\frac {1064}{3} x^{3}+656 x^{4}+\frac {5099}{5} x^{5}+\frac {2377}{2} x^{6}+1176 x^{7}+\frac {3415}{4} x^{8}+\frac {5075}{9} x^{9}+\frac {475}{2} x^{10}+\frac {1250}{11} x^{11}\) | \(55\) |
default | \(48 x +136 x^{2}+\frac {1064}{3} x^{3}+656 x^{4}+\frac {5099}{5} x^{5}+\frac {2377}{2} x^{6}+1176 x^{7}+\frac {3415}{4} x^{8}+\frac {5075}{9} x^{9}+\frac {475}{2} x^{10}+\frac {1250}{11} x^{11}\) | \(55\) |
norman | \(48 x +136 x^{2}+\frac {1064}{3} x^{3}+656 x^{4}+\frac {5099}{5} x^{5}+\frac {2377}{2} x^{6}+1176 x^{7}+\frac {3415}{4} x^{8}+\frac {5075}{9} x^{9}+\frac {475}{2} x^{10}+\frac {1250}{11} x^{11}\) | \(55\) |
risch | \(48 x +136 x^{2}+\frac {1064}{3} x^{3}+656 x^{4}+\frac {5099}{5} x^{5}+\frac {2377}{2} x^{6}+1176 x^{7}+\frac {3415}{4} x^{8}+\frac {5075}{9} x^{9}+\frac {475}{2} x^{10}+\frac {1250}{11} x^{11}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 54, normalized size = 0.79 \begin {gather*} \frac {1250}{11} \, x^{11} + \frac {475}{2} \, x^{10} + \frac {5075}{9} \, x^{9} + \frac {3415}{4} \, x^{8} + 1176 \, x^{7} + \frac {2377}{2} \, x^{6} + \frac {5099}{5} \, x^{5} + 656 \, x^{4} + \frac {1064}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 5.34, size = 54, normalized size = 0.79 \begin {gather*} \frac {1250}{11} \, x^{11} + \frac {475}{2} \, x^{10} + \frac {5075}{9} \, x^{9} + \frac {3415}{4} \, x^{8} + 1176 \, x^{7} + \frac {2377}{2} \, x^{6} + \frac {5099}{5} \, x^{5} + 656 \, x^{4} + \frac {1064}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 65, normalized size = 0.96 \begin {gather*} \frac {1250 x^{11}}{11} + \frac {475 x^{10}}{2} + \frac {5075 x^{9}}{9} + \frac {3415 x^{8}}{4} + 1176 x^{7} + \frac {2377 x^{6}}{2} + \frac {5099 x^{5}}{5} + 656 x^{4} + \frac {1064 x^{3}}{3} + 136 x^{2} + 48 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.55, size = 54, normalized size = 0.79 \begin {gather*} \frac {1250}{11} \, x^{11} + \frac {475}{2} \, x^{10} + \frac {5075}{9} \, x^{9} + \frac {3415}{4} \, x^{8} + 1176 \, x^{7} + \frac {2377}{2} \, x^{6} + \frac {5099}{5} \, x^{5} + 656 \, x^{4} + \frac {1064}{3} \, x^{3} + 136 \, x^{2} + 48 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.06, size = 54, normalized size = 0.79 \begin {gather*} \frac {1250\,x^{11}}{11}+\frac {475\,x^{10}}{2}+\frac {5075\,x^9}{9}+\frac {3415\,x^8}{4}+1176\,x^7+\frac {2377\,x^6}{2}+\frac {5099\,x^5}{5}+656\,x^4+\frac {1064\,x^3}{3}+136\,x^2+48\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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