Optimal. Leaf size=18 \[ \frac{x^3}{3}+\frac{3 x^2}{2}-7 x \]
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Rubi [A] time = 0.0103565, antiderivative size = 18, normalized size of antiderivative = 1., 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*}
Mathematica [A] time = 0.0006199, size = 18, normalized size = 1. \[ \frac{x^3}{3}+\frac{3 x^2}{2}-7 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 28, normalized size = 1.6 \begin{align*}{\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 \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.64185, size = 19, normalized size = 1.06 \begin{align*} \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} - 7 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Exception raised: UnboundLocalError} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.051822, size = 14, normalized size = 0.78 \begin{align*} \frac{x^{3}}{3} + \frac{3 x^{2}}{2} - 7 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.12858, size = 19, normalized size = 1.06 \begin{align*} \frac{1}{3} \, x^{3} + \frac{3}{2} \, x^{2} - 7 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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