Optimal. Leaf size=13 \[ \text {Int}\left (\frac {x^m}{\cosh ^{-1}(a x)^2},x\right ) \]
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Rubi [A] time = 0.02, 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 = {} \[ \int \frac {x^m}{\cosh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {x^m}{\cosh ^{-1}(a x)^2} \, dx &=\int \frac {x^m}{\cosh ^{-1}(a x)^2} \, dx\\ \end {align*}
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Mathematica [A] time = 1.34, size = 0, normalized size = 0.00 \[ \int \frac {x^m}{\cosh ^{-1}(a x)^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.46, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {x^{m}}{\operatorname {arcosh}\left (a x\right )^{2}}, x\right ) \]
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 \[ \int \frac {x^{m}}{\operatorname {arcosh}\left (a x\right )^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.87, size = 0, normalized size = 0.00 \[ \int \frac {x^{m}}{\mathrm {arccosh}\left (a x \right )^{2}}\, dx \]
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 \[ -\frac {{\left (a^{2} x^{2} - 1\right )} \sqrt {a x + 1} \sqrt {a x - 1} x^{m} + {\left (a^{3} x^{3} - a x\right )} x^{m}}{{\left (a^{3} x^{2} + \sqrt {a x + 1} \sqrt {a x - 1} a^{2} x - a\right )} \log \left (a x + \sqrt {a x + 1} \sqrt {a x - 1}\right )} + \int \frac {{\left (a^{3} {\left (m + 1\right )} x^{3} - a {\left (m - 1\right )} x\right )} {\left (a x + 1\right )} {\left (a x - 1\right )} x^{m} + {\left (2 \, a^{4} {\left (m + 1\right )} x^{4} - a^{2} {\left (3 \, m + 1\right )} x^{2} + m\right )} \sqrt {a x + 1} \sqrt {a x - 1} x^{m} + {\left (a^{5} {\left (m + 1\right )} x^{5} - 2 \, a^{3} {\left (m + 1\right )} x^{3} + a {\left (m + 1\right )} x\right )} x^{m}}{{\left (a^{5} x^{5} + {\left (a x + 1\right )} {\left (a x - 1\right )} a^{3} x^{3} - 2 \, a^{3} x^{3} + 2 \, {\left (a^{4} x^{4} - a^{2} x^{2}\right )} \sqrt {a x + 1} \sqrt {a x - 1} + a x\right )} \log \left (a x + \sqrt {a x + 1} \sqrt {a x - 1}\right )}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.08 \[ \int \frac {x^m}{{\mathrm {acosh}\left (a\,x\right )}^2} \,d x \]
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 \[ \int \frac {x^{m}}{\operatorname {acosh}^{2}{\left (a x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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