Optimal. Leaf size=23 \[ \text {Int}\left (x^m \text {csch}^3(a+b x) \text {sech}^2(a+b x),x\right ) \]
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Rubi [A] time = 0.60, 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 = {} \[ \int x^m \text {csch}^3(a+b x) \text {sech}^2(a+b x) \, dx \]
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}^2(a+b x) \, dx &=\int x^m \text {csch}^3(a+b x) \text {sech}^2(a+b x) \, dx\\ \end {align*}
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Mathematica [A] time = 69.16, size = 0, normalized size = 0.00 \[ \int x^m \text {csch}^3(a+b x) \text {sech}^2(a+b x) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (x^{m} \operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{2}, x\right ) \]
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 \[ \int x^{m} \operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.24, size = 0, normalized size = 0.00 \[ \int x^{m} \mathrm {csch}\left (b x +a \right )^{3} \mathrm {sech}\left (b x +a \right )^{2}\, dx \]
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 \[ \int x^{m} \operatorname {csch}\left (b x + a\right )^{3} \operatorname {sech}\left (b x + a\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {x^m}{{\mathrm {cosh}\left (a+b\,x\right )}^2\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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 \[ \int x^{m} \operatorname {csch}^{3}{\left (a + b x \right )} \operatorname {sech}^{2}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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