Optimal. Leaf size=63 \[ \frac {9}{8} \text {Int}\left (\frac {\sinh ^{\frac {3}{2}}(x)}{x},x\right )+\frac {3}{8} \text {Int}\left (\frac {1}{x \sqrt {\sinh (x)}},x\right )-\frac {\sinh ^{\frac {3}{2}}(x)}{2 x^2}-\frac {3 \sqrt {\sinh (x)} \cosh (x)}{4 x} \]
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Rubi [A] time = 0.11, 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 = {} \[ \int \frac {\sinh ^{\frac {3}{2}}(x)}{x^3} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\sinh ^{\frac {3}{2}}(x)}{x^3} \, dx &=-\frac {3 \cosh (x) \sqrt {\sinh (x)}}{4 x}-\frac {\sinh ^{\frac {3}{2}}(x)}{2 x^2}+\frac {3}{8} \int \frac {1}{x \sqrt {\sinh (x)}} \, dx+\frac {9}{8} \int \frac {\sinh ^{\frac {3}{2}}(x)}{x} \, dx\\ \end {align*}
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Mathematica [A] time = 6.04, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^{\frac {3}{2}}(x)}{x^3} \, dx \]
Verification is Not applicable to the result.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: TypeError} \]
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 \[ \int \frac {\sinh \relax (x)^{\frac {3}{2}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [F(-2)] time = 180.00, size = 0, normalized size = 0.00 \[ \int \frac {\sinh ^{\frac {3}{2}}\relax (x )}{x^{3}}\, dx \]
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 \[ \int \frac {\sinh \relax (x)^{\frac {3}{2}}}{x^{3}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {{\mathrm {sinh}\relax (x)}^{3/2}}{x^3} \,d x \]
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 \[ \int \frac {\sinh ^{\frac {3}{2}}{\relax (x )}}{x^{3}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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