Optimal. Leaf size=25 \[ -\frac {9}{x}+22 x-4 x^2+\frac {x^3}{3}-24 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 25, 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^3}{3}-4 x^2+22 x-\frac {9}{x}-24 \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^2} \, dx &=\int \left (22+\frac {9}{x^2}-\frac {24}{x}-8 x+x^2\right ) \, dx\\ &=-\frac {9}{x}+22 x-4 x^2+\frac {x^3}{3}-24 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} -\frac {9}{x}+22 x-4 x^2+\frac {x^3}{3}-24 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.64, size = 24, normalized size = 0.96
method | result | size |
default | \(-\frac {9}{x}+22 x -4 x^{2}+\frac {x^{3}}{3}-24 \ln \left (x \right )\) | \(24\) |
risch | \(-\frac {9}{x}+22 x -4 x^{2}+\frac {x^{3}}{3}-24 \ln \left (x \right )\) | \(24\) |
norman | \(\frac {-9+22 x^{2}-4 x^{3}+\frac {1}{3} x^{4}}{x}-24 \ln \left (x \right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 23, normalized size = 0.92 \begin {gather*} \frac {1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac {9}{x} - 24 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.68, size = 25, normalized size = 1.00 \begin {gather*} \frac {x^{4} - 12 \, x^{3} + 66 \, x^{2} - 72 \, x \log \left (x\right ) - 27}{3 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 20, normalized size = 0.80 \begin {gather*} \frac {x^{3}}{3} - 4 x^{2} + 22 x - 24 \log {\left (x \right )} - \frac {9}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.32, size = 24, normalized size = 0.96 \begin {gather*} \frac {1}{3} \, x^{3} - 4 \, x^{2} + 22 \, x - \frac {9}{x} - 24 \, \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 = 0.92 \begin {gather*} 22\,x-24\,\ln \left (x\right )-\frac {9}{x}-4\,x^2+\frac {x^3}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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