Optimal. Leaf size=27 \[ \frac {2}{-2 x-x^2 (2+4 x)^2-x \log \left (x^2\right )} \]
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Rubi [A] time = 0.49, antiderivative size = 26, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 3, integrand size = 96, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6688, 12, 6687} \begin {gather*} -\frac {2}{x \left (16 x^3+16 x^2+\log \left (x^2\right )+4 x+2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6687
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (4+8 x+48 x^2+64 x^3+\log \left (x^2\right )\right )}{x^2 \left (2+4 x+16 x^2+16 x^3+\log \left (x^2\right )\right )^2} \, dx\\ &=2 \int \frac {4+8 x+48 x^2+64 x^3+\log \left (x^2\right )}{x^2 \left (2+4 x+16 x^2+16 x^3+\log \left (x^2\right )\right )^2} \, dx\\ &=-\frac {2}{x \left (2+4 x+16 x^2+16 x^3+\log \left (x^2\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.68, size = 26, normalized size = 0.96 \begin {gather*} -\frac {2}{x \left (2+4 x+16 x^2+16 x^3+\log \left (x^2\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 29, normalized size = 1.07 \begin {gather*} -\frac {2}{16 \, x^{4} + 16 \, x^{3} + 4 \, x^{2} + x \log \left (x^{2}\right ) + 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 29, normalized size = 1.07 \begin {gather*} -\frac {2}{16 \, x^{4} + 16 \, x^{3} + 4 \, x^{2} + x \log \left (x^{2}\right ) + 2 \, x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 27, normalized size = 1.00
method | result | size |
risch | \(-\frac {2}{x \left (16 x^{3}+16 x^{2}+\ln \left (x^{2}\right )+4 x +2\right )}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 25, normalized size = 0.93 \begin {gather*} -\frac {1}{8 \, x^{4} + 8 \, x^{3} + 2 \, x^{2} + x \log \relax (x) + x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {16\,x+2\,\ln \left (x^2\right )+96\,x^2+128\,x^3+8}{4\,x^2+16\,x^3+80\,x^4+192\,x^5+384\,x^6+512\,x^7+256\,x^8+x^2\,{\ln \left (x^2\right )}^2+\ln \left (x^2\right )\,\left (32\,x^5+32\,x^4+8\,x^3+4\,x^2\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.14, size = 27, normalized size = 1.00 \begin {gather*} - \frac {2}{16 x^{4} + 16 x^{3} + 4 x^{2} + x \log {\left (x^{2} \right )} + 2 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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