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 = 0.01, 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 = {}
\begin {gather*} \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \end {gather*}
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 {\text {Subst}(\int F(c,d,x,r,s) \, dx,x,\coth (a+b x))}{b}\\ \end {align*}
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Mathematica [A]
time = 0.06, size = 0, normalized size = 0.00 \begin {gather*} \int \text {csch}^2(a+b x) F(c,d,\coth (a+b x),r,s) \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.46, 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 \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 F{\left (c,d,\coth {\left (a + b x \right )},r,s \right )} \operatorname {csch}^{2}{\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 = -0.04 \begin {gather*} \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 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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