Optimal. Leaf size=27 \[ -24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 1, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {712}
\begin {gather*} \frac {x^4}{4}-\frac {8 x^3}{3}+11 x^2-24 x+9 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 712
Rubi steps
\begin {align*} \int \frac {\left (3-4 x+x^2\right )^2}{x} \, dx &=\int \left (-24+\frac {9}{x}+22 x-8 x^2+x^3\right ) \, dx\\ &=-24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 27, normalized size = 1.00 \begin {gather*} -24 x+11 x^2-\frac {8 x^3}{3}+\frac {x^4}{4}+9 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.69, size = 24, normalized size = 0.89
method | result | size |
default | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
norman | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
risch | \(-24 x +11 x^{2}-\frac {8 x^{3}}{3}+\frac {x^{4}}{4}+9 \ln \left (x \right )\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 23, normalized size = 0.85 \begin {gather*} \frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.83, size = 23, normalized size = 0.85 \begin {gather*} \frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 24, normalized size = 0.89 \begin {gather*} \frac {x^{4}}{4} - \frac {8 x^{3}}{3} + 11 x^{2} - 24 x + 9 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.36, size = 24, normalized size = 0.89 \begin {gather*} \frac {1}{4} \, x^{4} - \frac {8}{3} \, x^{3} + 11 \, x^{2} - 24 \, x + 9 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.02, size = 23, normalized size = 0.85 \begin {gather*} 9\,\ln \left (x\right )-24\,x+11\,x^2-\frac {8\,x^3}{3}+\frac {x^4}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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