Optimal. Leaf size=19 \[ \text {Int}\left (\frac {\text {csch}^2(a+b x)}{c+d x},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx &=\int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx\\ \end {align*}
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Mathematica [A] time = 17.00, size = 0, normalized size = 0.00 \[ \int \frac {\text {csch}^2(a+b x)}{c+d x} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c}, x\right ) \]
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 \[ \int \frac {\operatorname {csch}\left (b x + a\right )^{2}}{d x + c}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 0, normalized size = 0.00 \[ \int \frac {\mathrm {csch}\left (b x +a \right )^{2}}{d x +c}\, dx \]
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 \[ 4 \, d \int \frac {1}{4 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} + {\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} - 4 \, d \int -\frac {1}{4 \, {\left (b d^{2} x^{2} + 2 \, b c d x + b c^{2} - {\left (b d^{2} x^{2} e^{a} + 2 \, b c d x e^{a} + b c^{2} e^{a}\right )} e^{\left (b x\right )}\right )}}\,{d x} + \frac {2}{b d x + b c - {\left (b d x e^{\left (2 \, a\right )} + b c e^{\left (2 \, a\right )}\right )} e^{\left (2 \, b x\right )}} \]
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 \[ \int \frac {1}{{\mathrm {sinh}\left (a+b\,x\right )}^2\,\left (c+d\,x\right )} \,d x \]
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 \[ \int \frac {\operatorname {csch}^{2}{\left (a + b x \right )}}{c + d x}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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