Optimal. Leaf size=15 \[ \text {Int}\left (\frac {1}{\left (2-\log \left (x^2+1\right )\right )^5},x\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx &=\int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx\\ \end {align*}
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Mathematica [A] time = 0.24, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.42, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {1}{\log \left (x^{2} + 1\right )^{5} - 10 \, \log \left (x^{2} + 1\right )^{4} + 40 \, \log \left (x^{2} + 1\right )^{3} - 80 \, \log \left (x^{2} + 1\right )^{2} + 80 \, \log \left (x^{2} + 1\right ) - 32}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int -\frac {1}{{\left (\log \left (x^{2} + 1\right ) - 2\right )}^{5}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 0, normalized size = 0.00 \[ \int \frac {1}{\left (-\ln \left (x^{2}+1\right )+2\right )^{5}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \frac {32 \, x^{8} + 56 \, x^{6} + 120 \, x^{4} + {\left (x^{8} - 10 \, x^{4} - 24 \, x^{2} - 15\right )} \log \left (x^{2} + 1\right )^{3} - 2 \, {\left (2 \, x^{8} - x^{6} - 33 \, x^{4} - 75 \, x^{2} - 45\right )} \log \left (x^{2} + 1\right )^{2} + 216 \, x^{2} + 4 \, {\left (3 \, x^{8} - 2 \, x^{6} - 38 \, x^{4} - 78 \, x^{2} - 45\right )} \log \left (x^{2} + 1\right ) + 120}{384 \, {\left (x^{7} \log \left (x^{2} + 1\right )^{4} - 8 \, x^{7} \log \left (x^{2} + 1\right )^{3} + 24 \, x^{7} \log \left (x^{2} + 1\right )^{2} - 32 \, x^{7} \log \left (x^{2} + 1\right ) + 16 \, x^{7}\right )}} - \int \frac {x^{8} + 30 \, x^{4} + 120 \, x^{2} + 105}{384 \, {\left (x^{8} \log \left (x^{2} + 1\right ) - 2 \, x^{8}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int -\frac {1}{{\left (\ln \left (x^2+1\right )-2\right )}^5} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ - \frac {\int \frac {120 x^{2}}{x^{8} \log {\left (x^{2} + 1 \right )} - 2 x^{8}}\, dx + \int \frac {30 x^{4}}{x^{8} \log {\left (x^{2} + 1 \right )} - 2 x^{8}}\, dx + \int \frac {x^{8}}{x^{8} \log {\left (x^{2} + 1 \right )} - 2 x^{8}}\, dx + \int \frac {105}{x^{8} \log {\left (x^{2} + 1 \right )} - 2 x^{8}}\, dx}{384} + \frac {\frac {2 x^{8}}{3} + \frac {7 x^{6}}{6} + \frac {5 x^{4}}{2} + \frac {9 x^{2}}{2} + \left (\frac {x^{8}}{48} - \frac {5 x^{4}}{24} - \frac {x^{2}}{2} - \frac {5}{16}\right ) \log {\left (x^{2} + 1 \right )}^{3} + \left (- \frac {x^{8}}{12} + \frac {x^{6}}{24} + \frac {11 x^{4}}{8} + \frac {25 x^{2}}{8} + \frac {15}{8}\right ) \log {\left (x^{2} + 1 \right )}^{2} + \left (\frac {x^{8}}{4} - \frac {x^{6}}{6} - \frac {19 x^{4}}{6} - \frac {13 x^{2}}{2} - \frac {15}{4}\right ) \log {\left (x^{2} + 1 \right )} + \frac {5}{2}}{8 x^{7} \log {\left (x^{2} + 1 \right )}^{4} - 64 x^{7} \log {\left (x^{2} + 1 \right )}^{3} + 192 x^{7} \log {\left (x^{2} + 1 \right )}^{2} - 256 x^{7} \log {\left (x^{2} + 1 \right )} + 128 x^{7}} \]
Verification of antiderivative is not currently implemented for this CAS.
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