Optimal. Leaf size=15 \[ \text {Int}\left (\frac {1}{\left (2-\log \left (1+x^2\right )\right )^5},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx \end {gather*}
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 = 2.64, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{\left (2-\log \left (1+x^2\right )\right )^5} \, dx \end {gather*}
Verification is not applicable to the result.
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Mathics [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {cought exception: maximum recursion depth exceeded} \end {gather*}
Warning: Unable to verify antiderivative.
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Maple [A]
time = 0.06, size = 0, normalized size = 0.00 \[\int \frac {1}{\left (2-\ln \left (x^{2}+1\right )\right )^{5}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.31, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} - \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}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] N/A
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Could not integrate} \end {gather*}
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 \begin {gather*} \int -\frac {1}{{\left (\ln \left (x^2+1\right )-2\right )}^5} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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