Optimal. Leaf size=20 \[ \left (3-\frac {2}{3-x}-x\right ) (3+x)^3 \]
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Rubi [A] time = 0.07, antiderivative size = 28, normalized size of antiderivative = 1.40, number of steps used = 4, number of rules used = 3, integrand size = 36, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1586, 27, 1620} \begin {gather*} -x^4-6 x^3+2 x^2+78 x-\frac {432}{3-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 27
Rule 1586
Rule 1620
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {(3+x)^2 \left (30-68 x+30 x^2-4 x^3\right )}{9-6 x+x^2} \, dx\\ &=\int \frac {(3+x)^2 \left (30-68 x+30 x^2-4 x^3\right )}{(-3+x)^2} \, dx\\ &=\int \left (78-\frac {432}{(-3+x)^2}+4 x-18 x^2-4 x^3\right ) \, dx\\ &=-\frac {432}{3-x}+78 x+2 x^2-6 x^3-x^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 30, normalized size = 1.50 \begin {gather*} -\frac {-459+243 x-72 x^2-20 x^3+3 x^4+x^5}{-3+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.47, size = 30, normalized size = 1.50 \begin {gather*} -\frac {x^{5} + 3 \, x^{4} - 20 \, x^{3} - 72 \, x^{2} + 234 \, x - 432}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 26, normalized size = 1.30 \begin {gather*} -x^{4} - 6 \, x^{3} + 2 \, x^{2} + 78 \, x + \frac {432}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.20, size = 27, normalized size = 1.35
method | result | size |
default | \(-x^{4}-6 x^{3}+2 x^{2}+78 x +\frac {432}{x -3}\) | \(27\) |
risch | \(-x^{4}-6 x^{3}+2 x^{2}+78 x +\frac {432}{x -3}\) | \(27\) |
gosper | \(-\frac {x^{5}+3 x^{4}-20 x^{3}-72 x^{2}+270}{x -3}\) | \(28\) |
norman | \(\frac {-x^{5}-3 x^{4}+20 x^{3}+72 x^{2}-270}{x -3}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 26, normalized size = 1.30 \begin {gather*} -x^{4} - 6 \, x^{3} + 2 \, x^{2} + 78 \, x + \frac {432}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 26, normalized size = 1.30 \begin {gather*} 78\,x+\frac {432}{x-3}+2\,x^2-6\,x^3-x^4 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 20, normalized size = 1.00 \begin {gather*} - x^{4} - 6 x^{3} + 2 x^{2} + 78 x + \frac {432}{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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