Optimal. Leaf size=29 \[ \text {Int}\left (\frac {\text {csch}^3(a+b x)}{x^2},x\right )+\text {Int}\left (\frac {\text {csch}(a+b x)}{x^2},x\right ) \]
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Rubi [A] time = 0.08, 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 = {} \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x^2} \, dx &=\int \frac {\text {csch}(a+b x)}{x^2} \, dx+\int \frac {\text {csch}^3(a+b x)}{x^2} \, dx\\ \end {align*}
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Mathematica [A] time = 45.88, size = 0, normalized size = 0.00 \[ \int \frac {\coth ^2(a+b x) \text {csch}(a+b x)}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.40, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}}, x\right ) \]
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 \[ \int \frac {\cosh \left (b x + a\right )^{2} \operatorname {csch}\left (b x + a\right )^{3}}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.04, size = 0, normalized size = 0.00 \[ \int \frac {\left (\cosh ^{2}\left (b x +a \right )\right ) \mathrm {csch}\left (b x +a \right )^{3}}{x^{2}}\, dx \]
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 \[ -\frac {{\left (b x e^{\left (3 \, a\right )} - 2 \, e^{\left (3 \, a\right )}\right )} e^{\left (3 \, b x\right )} + {\left (b x e^{a} + 2 \, e^{a}\right )} e^{\left (b x\right )}}{b^{2} x^{3} e^{\left (4 \, b x + 4 \, a\right )} - 2 \, b^{2} x^{3} e^{\left (2 \, b x + 2 \, a\right )} + b^{2} x^{3}} + 2 \, \int \frac {b^{2} x^{2} + 6}{4 \, {\left (b^{2} x^{4} e^{\left (b x + a\right )} + b^{2} x^{4}\right )}}\,{d x} + 2 \, \int \frac {b^{2} x^{2} + 6}{4 \, {\left (b^{2} x^{4} e^{\left (b x + a\right )} - b^{2} x^{4}\right )}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.03 \[ \int \frac {{\mathrm {cosh}\left (a+b\,x\right )}^2}{x^2\,{\mathrm {sinh}\left (a+b\,x\right )}^3} \,d x \]
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 \[ \int \frac {\cosh ^{2}{\left (a + b x \right )} \operatorname {csch}^{3}{\left (a + b x \right )}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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