Optimal. Leaf size=24 \[ \text{Unintegrable}\left (\frac{1}{x^{5/2} \left (a+b \text{csch}\left (c+d \sqrt{x}\right )\right )^2},x\right ) \]
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Rubi [A] time = 0.0271841, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., Rules used = {} \[ \int \frac{1}{x^{5/2} \left (a+b \text{csch}\left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x^{5/2} \left (a+b \text{csch}\left (c+d \sqrt{x}\right )\right )^2} \, dx &=\int \frac{1}{x^{5/2} \left (a+b \text{csch}\left (c+d \sqrt{x}\right )\right )^2} \, dx\\ \end{align*}
Mathematica [A] time = 67.4899, size = 0, normalized size = 0. \[ \int \frac{1}{x^{5/2} \left (a+b \text{csch}\left (c+d \sqrt{x}\right )\right )^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.152, size = 0, normalized size = 0. \begin{align*} \int{{x}^{-{\frac{5}{2}}} \left ( a+b{\rm csch} \left (c+d\sqrt{x}\right ) \right ) ^{-2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0., size = 0, normalized size = 0. \begin{align*} -\frac{2 \,{\left (6 \, a b^{2} +{\left (a^{3} d e^{\left (2 \, c\right )} + a b^{2} d e^{\left (2 \, c\right )}\right )} \sqrt{x} e^{\left (2 \, d \sqrt{x}\right )} - 2 \,{\left (3 \, b^{3} e^{c} -{\left (a^{2} b d e^{c} + b^{3} d e^{c}\right )} \sqrt{x}\right )} e^{\left (d \sqrt{x}\right )} -{\left (a^{3} d + a b^{2} d\right )} \sqrt{x}\right )}}{3 \,{\left ({\left (a^{5} d e^{\left (2 \, c\right )} + a^{3} b^{2} d e^{\left (2 \, c\right )}\right )} x^{2} e^{\left (2 \, d \sqrt{x}\right )} + 2 \,{\left (a^{4} b d e^{c} + a^{2} b^{3} d e^{c}\right )} x^{2} e^{\left (d \sqrt{x}\right )} -{\left (a^{5} d + a^{3} b^{2} d\right )} x^{2}\right )}} + \int -\frac{2 \,{\left (4 \, a b^{2} \sqrt{x} -{\left (4 \, b^{3} \sqrt{x} e^{c} -{\left (2 \, a^{2} b d e^{c} + b^{3} d e^{c}\right )} x\right )} e^{\left (d \sqrt{x}\right )}\right )}}{{\left (a^{5} d e^{\left (2 \, c\right )} + a^{3} b^{2} d e^{\left (2 \, c\right )}\right )} x^{\frac{7}{2}} e^{\left (2 \, d \sqrt{x}\right )} + 2 \,{\left (a^{4} b d e^{c} + a^{2} b^{3} d e^{c}\right )} x^{\frac{7}{2}} e^{\left (d \sqrt{x}\right )} -{\left (a^{5} d + a^{3} b^{2} d\right )} x^{\frac{7}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\frac{\sqrt{x}}{b^{2} x^{3} \operatorname{csch}\left (d \sqrt{x} + c\right )^{2} + 2 \, a b x^{3} \operatorname{csch}\left (d \sqrt{x} + c\right ) + a^{2} x^{3}}, x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{x^{\frac{5}{2}} \left (a + b \operatorname{csch}{\left (c + d \sqrt{x} \right )}\right )^{2}}\, dx \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 0., size = 0, normalized size = 0. \begin{align*} \int \frac{1}{{\left (b \operatorname{csch}\left (d \sqrt{x} + c\right ) + a\right )}^{2} x^{\frac{5}{2}}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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