Optimal. Leaf size=63 \[ -\frac {\cosh ^{\frac {3}{2}}(x)}{2 x^2}-\frac {3 \sqrt {\cosh (x)} \sinh (x)}{4 x}-\frac {3}{8} \text {Int}\left (\frac {1}{x \sqrt {\cosh (x)}},x\right )+\frac {9}{8} \text {Int}\left (\frac {\cosh ^{\frac {3}{2}}(x)}{x},x\right ) \]
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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 = {}
\begin {gather*} \int \frac {\cosh ^{\frac {3}{2}}(x)}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {\cosh ^{\frac {3}{2}}(x)}{x^3} \, dx &=-\frac {\cosh ^{\frac {3}{2}}(x)}{2 x^2}-\frac {3 \sqrt {\cosh (x)} \sinh (x)}{4 x}-\frac {3}{8} \int \frac {1}{x \sqrt {\cosh (x)}} \, dx+\frac {9}{8} \int \frac {\cosh ^{\frac {3}{2}}(x)}{x} \, dx\\ \end {align*}
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Mathematica [A]
time = 2.70, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh ^{\frac {3}{2}}(x)}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.21, size = 0, normalized size = 0.00 \[\int \frac {\cosh ^{\frac {3}{2}}\left (x \right )}{x^{3}}\, dx\]
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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \end {gather*}
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 \begin {gather*} \int \frac {\cosh ^{\frac {3}{2}}{\left (x \right )}}{x^{3}}\, dx \end {gather*}
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 \begin {gather*} \text {could not integrate} \end {gather*}
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 \begin {gather*} \int \frac {{\mathrm {cosh}\left (x\right )}^{3/2}}{x^3} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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