Optimal. Leaf size=29 \[ \text {Int}\left (\frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}},x\right ) \]
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Rubi [A] time = 0.09, 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 = {} \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx &=\int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx\\ \end {align*}
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Mathematica [A] time = 0.41, size = 0, normalized size = 0.00 \[ \int \frac {a+b \text {sech}^{-1}(c x)}{x \sqrt {1-c^4 x^4}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 1.08, size = 0, normalized size = 0.00 \[ {\rm integral}\left (-\frac {\sqrt {-c^{4} x^{4} + 1} {\left (b \operatorname {arsech}\left (c x\right ) + a\right )}}{c^{4} x^{5} - x}, x\right ) \]
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 \[ \int \frac {b \operatorname {arsech}\left (c x\right ) + a}{\sqrt {-c^{4} x^{4} + 1} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 3.20, size = 0, normalized size = 0.00 \[ \int \frac {a +b \,\mathrm {arcsech}\left (c x \right )}{x \sqrt {-c^{4} x^{4}+1}}\, dx \]
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 \[ -\frac {1}{4} \, a {\left (\log \left (\sqrt {-c^{4} x^{4} + 1} + 1\right ) - \log \left (\sqrt {-c^{4} x^{4} + 1} - 1\right )\right )} + b \int \frac {\log \left (\sqrt {\frac {1}{c x} + 1} \sqrt {\frac {1}{c x} - 1} + \frac {1}{c x}\right )}{\sqrt {-{\left (c^{2} x^{2} + 1\right )} {\left (c x + 1\right )} {\left (c x - 1\right )}} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {a+b\,\mathrm {acosh}\left (\frac {1}{c\,x}\right )}{x\,\sqrt {1-c^4\,x^4}} \,d x \]
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 \[ \int \frac {a + b \operatorname {asech}{\left (c x \right )}}{x \sqrt {- \left (c x - 1\right ) \left (c x + 1\right ) \left (c^{2} x^{2} + 1\right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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