Optimal. Leaf size=25 \[ -\frac {9}{4 x^4}+\frac {8}{x^3}-\frac {11}{x^2}+\frac {8}{x}+\log (x) \]
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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 {9}{4 x^4}+\frac {8}{x^3}-\frac {11}{x^2}+\frac {8}{x}+\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^5} \, dx &=\int \left (\frac {9}{x^5}-\frac {24}{x^4}+\frac {22}{x^3}-\frac {8}{x^2}+\frac {1}{x}\right ) \, dx\\ &=-\frac {9}{4 x^4}+\frac {8}{x^3}-\frac {11}{x^2}+\frac {8}{x}+\log (x)\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 25, normalized size = 1.00 \begin {gather*} -\frac {9}{4 x^4}+\frac {8}{x^3}-\frac {11}{x^2}+\frac {8}{x}+\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 |
norman | \(\frac {-\frac {9}{4}+8 x^{3}-11 x^{2}+8 x}{x^{4}}+\ln \left (x \right )\) | \(23\) |
risch | \(\frac {-\frac {9}{4}+8 x^{3}-11 x^{2}+8 x}{x^{4}}+\ln \left (x \right )\) | \(23\) |
default | \(-\frac {9}{4 x^{4}}+\frac {8}{x^{3}}-\frac {11}{x^{2}}+\frac {8}{x}+\ln \left (x \right )\) | \(24\) |
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 {32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 3.07, size = 27, normalized size = 1.08 \begin {gather*} \frac {4 \, x^{4} \log \left (x\right ) + 32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 22, normalized size = 0.88 \begin {gather*} \log {\left (x \right )} + \frac {32 x^{3} - 44 x^{2} + 32 x - 9}{4 x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.34, size = 24, normalized size = 0.96 \begin {gather*} \frac {32 \, x^{3} - 44 \, x^{2} + 32 \, x - 9}{4 \, x^{4}} + \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 = 22, normalized size = 0.88 \begin {gather*} \ln \left (x\right )+\frac {8\,x^3-11\,x^2+8\,x-\frac {9}{4}}{x^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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