Optimal. Leaf size=18 \[ \frac {x^3}{3}+\frac {3 x^2}{2}-7 x \]
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Rubi [A] time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {43} \[ \frac {x^3}{3}+\frac {3 x^2}{2}-7 x \]
Antiderivative was successfully verified.
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Rule 43
Rubi steps
\begin {align*} \int \left (\frac {1}{2} \left (3-\sqrt {37}\right )+x\right ) \left (\frac {1}{2} \left (3+\sqrt {37}\right )+x\right ) \, dx &=\int \left (-7+3 x+x^2\right ) \, dx\\ &=-7 x+\frac {3 x^2}{2}+\frac {x^3}{3}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 1.00 \[ \frac {x^3}{3}+\frac {3 x^2}{2}-7 x \]
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: SyntaxError} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.35, size = 14, normalized size = 0.78 \[ \frac {1}{3} \, x^{3} + \frac {3}{2} \, x^{2} - 7 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 28, normalized size = 1.56 \[ \frac {x^{3}}{3}+\frac {3 x^{2}}{2}+\left (\frac {3}{2}-\frac {\sqrt {37}}{2}\right ) \left (\frac {3}{2}+\frac {\sqrt {37}}{2}\right ) x \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.71, size = 14, normalized size = 0.78 \[ \frac {1}{3} \, x^{3} + \frac {3}{2} \, x^{2} - 7 \, x \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 13, normalized size = 0.72 \[ \frac {x\,\left (2\,x^2+9\,x-42\right )}{6} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 14, normalized size = 0.78 \[ \frac {x^{3}}{3} + \frac {3 x^{2}}{2} - 7 x \]
Verification of antiderivative is not currently implemented for this CAS.
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