Optimal. Leaf size=21 \[ \text {Int}\left (x^m \text {csch}^3(a+b x) \text {sech}(a+b x),x\right ) \]
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Rubi [A]
time = 0.40, 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 x^m \text {csch}^3(a+b x) \text {sech}(a+b x) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int x^m \text {csch}^3(a+b x) \text {sech}(a+b x) \, dx &=\int x^m \text {csch}^3(a+b x) \text {sech}(a+b x) \, dx\\ \end {align*}
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Mathematica [A]
time = 43.83, size = 0, normalized size = 0.00 \begin {gather*} \int x^m \text {csch}^3(a+b x) \text {sech}(a+b x) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.76, size = 0, normalized size = 0.00 \[\int x^{m} \mathrm {csch}\left (b x +a \right )^{3} \mathrm {sech}\left (b x +a \right )\, dx\]
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 x^{m} \operatorname {csch}^{3}{\left (a + b x \right )} \operatorname {sech}{\left (a + b 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 = -0.05 \begin {gather*} \int \frac {x^m}{\mathrm {cosh}\left (a+b\,x\right )\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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