Optimal. Leaf size=13 \[ \text {Int}\left (\frac {1}{a+b \text {sech}^{-1}(c x)},x\right ) \]
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Rubi [A] time = 0.01, 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 = {} \[ \int \frac {1}{a+b \text {sech}^{-1}(c x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{a+b \text {sech}^{-1}(c x)} \, dx &=\int \frac {1}{a+b \text {sech}^{-1}(c x)} \, dx\\ \end {align*}
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Mathematica [A] time = 0.03, size = 0, normalized size = 0.00 \[ \int \frac {1}{a+b \text {sech}^{-1}(c x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {1}{b \operatorname {arsech}\left (c x\right ) + a}, x\right ) \]
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 \[ \int \frac {1}{b \operatorname {arsech}\left (c x\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.49, size = 0, normalized size = 0.00 \[ \int \frac {1}{a +b \,\mathrm {arcsech}\left (c x \right )}\, dx \]
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 \[ \int \frac {1}{b \operatorname {arsech}\left (c x\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {1}{a+b\,\mathrm {acosh}\left (\frac {1}{c\,x}\right )} \,d x \]
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 \[ \int \frac {1}{a + b \operatorname {asech}{\left (c x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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