Optimal. Leaf size=33 \[ -\frac {\left (\frac {1}{4} (-2+x)+x\right )^2 \left (5-4 \left (4-\frac {5}{x}+x\right )^2\right )}{x}+\log (4) \]
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Rubi [A] time = 0.04, antiderivative size = 33, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {12, 14} \begin {gather*} \frac {25 x^3}{4}+\frac {25}{x^3}+45 x^2-\frac {165}{x^2}-\frac {149 x}{16}+\frac {361}{x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{16} \int \frac {-1200+5280 x-5776 x^2-149 x^4+1440 x^5+300 x^6}{x^4} \, dx\\ &=\frac {1}{16} \int \left (-149-\frac {1200}{x^4}+\frac {5280}{x^3}-\frac {5776}{x^2}+1440 x+300 x^2\right ) \, dx\\ &=\frac {25}{x^3}-\frac {165}{x^2}+\frac {361}{x}-\frac {149 x}{16}+45 x^2+\frac {25 x^3}{4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 33, normalized size = 1.00 \begin {gather*} \frac {25}{x^3}-\frac {165}{x^2}+\frac {361}{x}-\frac {149 x}{16}+45 x^2+\frac {25 x^3}{4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 30, normalized size = 0.91 \begin {gather*} \frac {100 \, x^{6} + 720 \, x^{5} - 149 \, x^{4} + 5776 \, x^{2} - 2640 \, x + 400}{16 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.56, size = 28, normalized size = 0.85 \begin {gather*} \frac {25}{4} \, x^{3} + 45 \, x^{2} - \frac {149}{16} \, x + \frac {361 \, x^{2} - 165 \, x + 25}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 30, normalized size = 0.91
method | result | size |
default | \(\frac {25 x^{3}}{4}+45 x^{2}-\frac {149 x}{16}-\frac {165}{x^{2}}+\frac {25}{x^{3}}+\frac {361}{x}\) | \(30\) |
norman | \(\frac {25-165 x +361 x^{2}-\frac {149}{16} x^{4}+45 x^{5}+\frac {25}{4} x^{6}}{x^{3}}\) | \(30\) |
risch | \(\frac {25 x^{3}}{4}+45 x^{2}-\frac {149 x}{16}+\frac {5776 x^{2}-2640 x +400}{16 x^{3}}\) | \(30\) |
gosper | \(\frac {100 x^{6}+720 x^{5}-149 x^{4}+5776 x^{2}-2640 x +400}{16 x^{3}}\) | \(31\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 28, normalized size = 0.85 \begin {gather*} \frac {25}{4} \, x^{3} + 45 \, x^{2} - \frac {149}{16} \, x + \frac {361 \, x^{2} - 165 \, x + 25}{x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 28, normalized size = 0.85 \begin {gather*} \frac {361\,x^2-165\,x+25}{x^3}-\frac {149\,x}{16}+45\,x^2+\frac {25\,x^3}{4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.08, size = 31, normalized size = 0.94 \begin {gather*} \frac {25 x^{3}}{4} + 45 x^{2} - \frac {149 x}{16} + \frac {5776 x^{2} - 2640 x + 400}{16 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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