Optimal. Leaf size=27 \[ \text {Int}\left (\frac {\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))},x\right ) \]
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Rubi [A] time = 0.06, 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 = {} \[ \int \frac {\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx &=\int \frac {\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx\\ \end {align*}
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Mathematica [A] time = 116.73, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^2(c+d x)}{x (a+b \cosh (c+d x))} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.58, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sinh \left (d x + c\right )^{2}}{b x \cosh \left (d x + c\right ) + a x}, x\right ) \]
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 \[ \int \frac {\sinh \left (d x + c\right )^{2}}{{\left (b \cosh \left (d x + c\right ) + a\right )} x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.29, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^{2}\left (d x +c \right )}{x \left (a +b \cosh \left (d x +c \right )\right )}\, dx \]
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 \[ 2 \, {\left (a^{2} e^{c} - b^{2} e^{c}\right )} \int \frac {e^{\left (d x\right )}}{b^{3} x e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a b^{2} x e^{\left (d x + c\right )} + b^{3} x}\,{d x} + \frac {{\rm Ei}\left (-d x\right ) e^{\left (-c\right )}}{2 \, b} + \frac {{\rm Ei}\left (d x\right ) e^{c}}{2 \, b} - \frac {a \log \relax (x)}{b^{2}} \]
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 \[ \int \frac {{\mathrm {sinh}\left (c+d\,x\right )}^2}{x\,\left (a+b\,\mathrm {cosh}\left (c+d\,x\right )\right )} \,d x \]
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 \[ \int \frac {\sinh ^{2}{\left (c + d x \right )}}{x \left (a + b \cosh {\left (c + d x \right )}\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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