Optimal. Leaf size=23 \[ \text {Int}\left (\text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s),x\right ) \]
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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 = {} \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx &=-\frac {\operatorname {Subst}(\int F(c,d,x,r,s) \, dx,x,\coth (a+b x))}{b}\\ \end {align*}
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Mathematica [A] time = 0.08, size = 0, normalized size = 0.00 \[ \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.41, size = 0, normalized size = 0.00 \[ {\rm integral}\left (F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2}, x\right ) \]
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 \[ \int F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 0, normalized size = 0.00 \[ \int \mathrm {csch}\left (b x +a \right )^{2} F \left (c , d , \coth \left (b x +a \right ), r , s\right )\, dx \]
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 \[ \int F\left (c, d, \coth \left (b x + a\right ), r, s\right ) \operatorname {csch}\left (b x + a\right )^{2}\,{d x} \]
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 \[ \int \frac {F\left (c,d,\mathrm {coth}\left (a+b\,x\right ),r,s\right )}{{\mathrm {sinh}\left (a+b\,x\right )}^2} \,d x \]
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 \[ \int F{\left (c,d,\coth {\left (a + b x \right )},r,s \right )} \operatorname {csch}^{2}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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