Optimal. Leaf size=22 \[ 21 x-4 x^3+\frac {1}{16} \left (7-4 x^2\right )^2 \]
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Rubi [A]
time = 0.00, antiderivative size = 22, normalized size of antiderivative = 1.00, 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 = {655}
\begin {gather*} -4 x^3+\frac {1}{16} \left (7-4 x^2\right )^2+21 x \end {gather*}
Antiderivative was successfully verified.
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Rule 655
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*}
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Mathematica [A]
time = 0.00, size = 19, normalized size = 0.86 \begin {gather*} 21 x-\frac {7 x^2}{2}-4 x^3+x^4 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 18, normalized size = 0.82
method | result | size |
gosper | \(x^{4}-4 x^{3}-\frac {7}{2} x^{2}+21 x\) | \(18\) |
default | \(x^{4}-4 x^{3}-\frac {7}{2} x^{2}+21 x\) | \(18\) |
norman | \(x^{4}-4 x^{3}-\frac {7}{2} x^{2}+21 x\) | \(18\) |
risch | \(x^{4}-4 x^{3}-\frac {7}{2} x^{2}+21 x\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 17, normalized size = 0.77 \begin {gather*} x^{4} - 4 \, x^{3} - \frac {7}{2} \, x^{2} + 21 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 17, normalized size = 0.77 \begin {gather*} x^{4} - 4 \, x^{3} - \frac {7}{2} \, x^{2} + 21 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.00, size = 17, normalized size = 0.77 \begin {gather*} x^{4} - 4 x^{3} - \frac {7 x^{2}}{2} + 21 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 3.42, size = 17, normalized size = 0.77 \begin {gather*} x^{4} - 4 \, x^{3} - \frac {7}{2} \, x^{2} + 21 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.03, size = 17, normalized size = 0.77 \begin {gather*} x^4-4\,x^3-\frac {7\,x^2}{2}+21\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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