Optimal. Leaf size=22 \[ -4 x^3+\frac{1}{16} \left (7-4 x^2\right )^2+21 x \]
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Rubi [A] time = 0.0042643, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {641} \[ -4 x^3+\frac{1}{16} \left (7-4 x^2\right )^2+21 x \]
Antiderivative was successfully verified.
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Rule 641
Rubi steps
\begin{align*} \int (-3+x) \left (-7+4 x^2\right ) \, dx &=\frac{1}{16} \left (7-4 x^2\right )^2-3 \int \left (-7+4 x^2\right ) \, dx\\ &=21 x-4 x^3+\frac{1}{16} \left (7-4 x^2\right )^2\\ \end{align*}
Mathematica [A] time = 0.0009434, size = 19, normalized size = 0.86 \[ x^4-4 x^3-\frac{7 x^2}{2}+21 x \]
Antiderivative was successfully verified.
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Maple [A] time = 0., size = 18, normalized size = 0.8 \begin{align*}{x}^{4}-4\,{x}^{3}-{\frac{7\,{x}^{2}}{2}}+21\,x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 1.11595, size = 23, normalized size = 1.05 \begin{align*} x^{4} - 4 \, x^{3} - \frac{7}{2} \, x^{2} + 21 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.13045, size = 41, normalized size = 1.86 \begin{align*} x^{4} - 4 x^{3} - \frac{7}{2} x^{2} + 21 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.051037, size = 17, normalized size = 0.77 \begin{align*} x^{4} - 4 x^{3} - \frac{7 x^{2}}{2} + 21 x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14309, size = 23, normalized size = 1.05 \begin{align*} x^{4} - 4 \, x^{3} - \frac{7}{2} \, x^{2} + 21 \, x \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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