Optimal. Leaf size=49 \[ \frac {3}{4} \text {Shi}\left (2 \tanh ^{-1}(a x)\right )+\frac {1}{8} \text {Shi}\left (4 \tanh ^{-1}(a x)\right )-\text {Int}\left (\frac {1}{x \left (-1+a^2 x^2\right ) \tanh ^{-1}(a x)},x\right ) \]
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Rubi [A]
time = 0.05, 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}{x \left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x \left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx &=\int \frac {1}{x \left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx\\ \end {align*}
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Mathematica [A]
time = 0.89, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{x \left (1-a^2 x^2\right )^3 \tanh ^{-1}(a x)} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 7.00, size = 0, normalized size = 0.00 \[\int \frac {1}{x \left (-a^{2} x^{2}+1\right )^{3} \arctanh \left (a x \right )}\, dx\]
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 = 0.00, 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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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} - \int \frac {1}{a^{6} x^{7} \operatorname {atanh}{\left (a x \right )} - 3 a^{4} x^{5} \operatorname {atanh}{\left (a x \right )} + 3 a^{2} x^{3} \operatorname {atanh}{\left (a x \right )} - x \operatorname {atanh}{\left (a x \right )}}\, dx \end {gather*}
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 \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 = -0.02 \begin {gather*} -\int \frac {1}{x\,\mathrm {atanh}\left (a\,x\right )\,{\left (a^2\,x^2-1\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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