Optimal. Leaf size=21 \[ -\frac {3}{x^3}+\frac {12}{x^2}-\frac {22}{x}+x-8 \log (x) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, 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 {3}{x^3}+\frac {12}{x^2}+x-\frac {22}{x}-8 \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^4} \, dx &=\int \left (1+\frac {9}{x^4}-\frac {24}{x^3}+\frac {22}{x^2}-\frac {8}{x}\right ) \, dx\\ &=-\frac {3}{x^3}+\frac {12}{x^2}-\frac {22}{x}+x-8 \log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 21, normalized size = 1.00 \begin {gather*} -\frac {3}{x^3}+\frac {12}{x^2}-\frac {22}{x}+x-8 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.64, size = 22, normalized size = 1.05
method | result | size |
risch | \(x +\frac {-22 x^{2}+12 x -3}{x^{3}}-8 \ln \left (x \right )\) | \(21\) |
default | \(-\frac {3}{x^{3}}+\frac {12}{x^{2}}-\frac {22}{x}+x -8 \ln \left (x \right )\) | \(22\) |
norman | \(\frac {x^{4}-22 x^{2}+12 x -3}{x^{3}}-8 \ln \left (x \right )\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 21, normalized size = 1.00 \begin {gather*} x - \frac {22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 2.80, size = 24, normalized size = 1.14 \begin {gather*} \frac {x^{4} - 8 \, x^{3} \log \left (x\right ) - 22 \, x^{2} + 12 \, x - 3}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 19, normalized size = 0.90 \begin {gather*} x - 8 \log {\left (x \right )} + \frac {- 22 x^{2} + 12 x - 3}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.35, size = 22, normalized size = 1.05 \begin {gather*} x - \frac {22 \, x^{2} - 12 \, x + 3}{x^{3}} - 8 \, \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 = 0.03, size = 21, normalized size = 1.00 \begin {gather*} x-8\,\ln \left (x\right )-\frac {22\,x^2-12\,x+3}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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