Optimal. Leaf size=23 \[ \text{Unintegrable}\left (\frac{1}{x (a+i a \sinh (c+d x))^{5/2}},x\right ) \]
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Rubi [A] time = 0.0900751, 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 = {} \[ \int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx &=\int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx\\ \end{align*}
Mathematica [A] time = 35.33, size = 0, normalized size = 0. \[ \int \frac{1}{x (a+i a \sinh (c+d x))^{5/2}} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.046, size = 0, normalized size = 0. \begin{align*} \int{\frac{1}{x} \left ( a+ia\sinh \left ( dx+c \right ) \right ) ^{-{\frac{5}{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*} \int \frac{1}{{\left (i \, a \sinh \left (d x + c\right ) + a\right )}^{\frac{5}{2}} x}\,{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*} \frac{\sqrt{\frac{1}{2}}{\left ({\left (-9 i \, d^{3} x^{3} + 18 i \, d^{2} x^{2} + 8 i \, d x - 48 i\right )} e^{\left (4 \, d x + 4 \, c\right )} -{\left (33 \, d^{3} x^{3} - 70 \, d^{2} x^{2} - 8 \, d x + 144\right )} e^{\left (3 \, d x + 3 \, c\right )} +{\left (-33 i \, d^{3} x^{3} - 70 i \, d^{2} x^{2} + 8 i \, d x + 144 i\right )} e^{\left (2 \, d x + 2 \, c\right )} -{\left (9 \, d^{3} x^{3} + 18 \, d^{2} x^{2} - 8 \, d x - 48\right )} e^{\left (d x + c\right )}\right )} \sqrt{i \, a e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a e^{\left (d x + c\right )} - i \, a} e^{\left (-\frac{1}{2} \, d x - \frac{1}{2} \, c\right )} +{\left (24 \, a^{3} d^{4} x^{4} e^{\left (5 \, d x + 5 \, c\right )} - 120 i \, a^{3} d^{4} x^{4} e^{\left (4 \, d x + 4 \, c\right )} - 240 \, a^{3} d^{4} x^{4} e^{\left (3 \, d x + 3 \, c\right )} + 240 i \, a^{3} d^{4} x^{4} e^{\left (2 \, d x + 2 \, c\right )} + 120 \, a^{3} d^{4} x^{4} e^{\left (d x + c\right )} - 24 i \, a^{3} d^{4} x^{4}\right )}{\rm integral}\left (\frac{\sqrt{\frac{1}{2}}{\left (-9 i \, d^{4} x^{4} + 80 i \, d^{2} x^{2} - 384 i\right )} \sqrt{i \, a e^{\left (2 \, d x + 2 \, c\right )} + 2 \, a e^{\left (d x + c\right )} - i \, a} e^{\left (\frac{1}{2} \, d x + \frac{1}{2} \, c\right )}}{48 \, a^{3} d^{4} x^{5} e^{\left (2 \, d x + 2 \, c\right )} - 96 i \, a^{3} d^{4} x^{5} e^{\left (d x + c\right )} - 48 \, a^{3} d^{4} x^{5}}, x\right )}{24 \, a^{3} d^{4} x^{4} e^{\left (5 \, d x + 5 \, c\right )} - 120 i \, a^{3} d^{4} x^{4} e^{\left (4 \, d x + 4 \, c\right )} - 240 \, a^{3} d^{4} x^{4} e^{\left (3 \, d x + 3 \, c\right )} + 240 i \, a^{3} d^{4} x^{4} e^{\left (2 \, d x + 2 \, c\right )} + 120 \, a^{3} d^{4} x^{4} e^{\left (d x + c\right )} - 24 i \, a^{3} d^{4} x^{4}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [F(-1)] time = 0., size = 0, normalized size = 0. \begin{align*} \text{Timed out} \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 (i \, a \sinh \left (d x + c\right ) + a\right )}^{\frac{5}{2}} x}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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