Optimal. Leaf size=30 \[ 2 x^5+\frac {x^4}{4}+\frac {16 x^3}{3}+\frac {7 x^2}{2}+6 x \]
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Rubi [A] time = 0.02, antiderivative size = 30, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 21, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {1657} \begin {gather*} 2 x^5+\frac {x^4}{4}+\frac {16 x^3}{3}+\frac {7 x^2}{2}+6 x \end {gather*}
Antiderivative was successfully verified.
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Rule 1657
Rubi steps
\begin {align*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right ) \, dx &=\int \left (6+7 x+16 x^2+x^3+10 x^4\right ) \, dx\\ &=6 x+\frac {7 x^2}{2}+\frac {16 x^3}{3}+\frac {x^4}{4}+2 x^5\\ \end {align*}
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Mathematica [A] time = 0.00, size = 30, normalized size = 1.00 \begin {gather*} 2 x^5+\frac {x^4}{4}+\frac {16 x^3}{3}+\frac {7 x^2}{2}+6 x \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \left (3-x+2 x^2\right ) \left (2+3 x+5 x^2\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.34, size = 24, normalized size = 0.80 \begin {gather*} 2 x^{5} + \frac {1}{4} x^{4} + \frac {16}{3} x^{3} + \frac {7}{2} x^{2} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 24, normalized size = 0.80 \begin {gather*} 2 \, x^{5} + \frac {1}{4} \, x^{4} + \frac {16}{3} \, x^{3} + \frac {7}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 25, normalized size = 0.83 \begin {gather*} 2 x^{5}+\frac {1}{4} x^{4}+\frac {16}{3} x^{3}+\frac {7}{2} x^{2}+6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 24, normalized size = 0.80 \begin {gather*} 2 \, x^{5} + \frac {1}{4} \, x^{4} + \frac {16}{3} \, x^{3} + \frac {7}{2} \, x^{2} + 6 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 24, normalized size = 0.80 \begin {gather*} 2\,x^5+\frac {x^4}{4}+\frac {16\,x^3}{3}+\frac {7\,x^2}{2}+6\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 26, normalized size = 0.87 \begin {gather*} 2 x^{5} + \frac {x^{4}}{4} + \frac {16 x^{3}}{3} + \frac {7 x^{2}}{2} + 6 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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