Optimal. Leaf size=46 \[ 18 x+\frac {15 x^2}{2}+\frac {53 x^3}{3}+\frac {x^4}{4}+\frac {61 x^5}{5}-\frac {4 x^6}{3}+\frac {20 x^7}{7} \]
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Rubi [A]
time = 0.02, antiderivative size = 46, 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 {20 x^7}{7}-\frac {4 x^6}{3}+\frac {61 x^5}{5}+\frac {x^4}{4}+\frac {53 x^3}{3}+\frac {15 x^2}{2}+18 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 ) \, dx &=\int \left (18+15 x+53 x^2+x^3+61 x^4-8 x^5+20 x^6\right ) \, dx\\ &=18 x+\frac {15 x^2}{2}+\frac {53 x^3}{3}+\frac {x^4}{4}+\frac {61 x^5}{5}-\frac {4 x^6}{3}+\frac {20 x^7}{7}\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 46, normalized size = 1.00 \begin {gather*} 18 x+\frac {15 x^2}{2}+\frac {53 x^3}{3}+\frac {x^4}{4}+\frac {61 x^5}{5}-\frac {4 x^6}{3}+\frac {20 x^7}{7} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 35, normalized size = 0.76
method | result | size |
gosper | \(18 x +\frac {15}{2} x^{2}+\frac {53}{3} x^{3}+\frac {1}{4} x^{4}+\frac {61}{5} x^{5}-\frac {4}{3} x^{6}+\frac {20}{7} x^{7}\) | \(35\) |
default | \(18 x +\frac {15}{2} x^{2}+\frac {53}{3} x^{3}+\frac {1}{4} x^{4}+\frac {61}{5} x^{5}-\frac {4}{3} x^{6}+\frac {20}{7} x^{7}\) | \(35\) |
norman | \(18 x +\frac {15}{2} x^{2}+\frac {53}{3} x^{3}+\frac {1}{4} x^{4}+\frac {61}{5} x^{5}-\frac {4}{3} x^{6}+\frac {20}{7} x^{7}\) | \(35\) |
risch | \(18 x +\frac {15}{2} x^{2}+\frac {53}{3} x^{3}+\frac {1}{4} x^{4}+\frac {61}{5} x^{5}-\frac {4}{3} x^{6}+\frac {20}{7} x^{7}\) | \(35\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 34, normalized size = 0.74 \begin {gather*} \frac {20}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {61}{5} \, x^{5} + \frac {1}{4} \, x^{4} + \frac {53}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.55, size = 34, normalized size = 0.74 \begin {gather*} \frac {20}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {61}{5} \, x^{5} + \frac {1}{4} \, x^{4} + \frac {53}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 41, normalized size = 0.89 \begin {gather*} \frac {20 x^{7}}{7} - \frac {4 x^{6}}{3} + \frac {61 x^{5}}{5} + \frac {x^{4}}{4} + \frac {53 x^{3}}{3} + \frac {15 x^{2}}{2} + 18 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.31, size = 34, normalized size = 0.74 \begin {gather*} \frac {20}{7} \, x^{7} - \frac {4}{3} \, x^{6} + \frac {61}{5} \, x^{5} + \frac {1}{4} \, x^{4} + \frac {53}{3} \, x^{3} + \frac {15}{2} \, x^{2} + 18 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 34, normalized size = 0.74 \begin {gather*} \frac {20\,x^7}{7}-\frac {4\,x^6}{3}+\frac {61\,x^5}{5}+\frac {x^4}{4}+\frac {53\,x^3}{3}+\frac {15\,x^2}{2}+18\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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