Optimal. Leaf size=17 \[ \text {Int}\left (\frac {1}{x^2 (a \cosh (x)+a)^{3/2}},x\right ) \]
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Rubi [A] time = 0.07, 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 = {} \[ \int \frac {1}{x^2 (a+a \cosh (x))^{3/2}} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {1}{x^2 (a+a \cosh (x))^{3/2}} \, dx &=\int \frac {1}{x^2 (a+a \cosh (x))^{3/2}} \, dx\\ \end {align*}
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Mathematica [A] time = 10.68, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^2 (a+a \cosh (x))^{3/2}} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.48, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\sqrt {a \cosh \relax (x) + a}}{a^{2} x^{2} \cosh \relax (x)^{2} + 2 \, a^{2} x^{2} \cosh \relax (x) + a^{2} x^{2}}, x\right ) \]
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 \[ \int \frac {1}{{\left (a \cosh \relax (x) + a\right )}^{\frac {3}{2}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 0, normalized size = 0.00 \[ \int \frac {1}{x^{2} \left (a +a \cosh \relax (x )\right )^{\frac {3}{2}}}\, dx \]
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 \[ \int \frac {1}{{\left (a \cosh \relax (x) + a\right )}^{\frac {3}{2}} x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.06 \[ \int \frac {1}{x^2\,{\left (a+a\,\mathrm {cosh}\relax (x)\right )}^{3/2}} \,d x \]
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 \[ \int \frac {1}{x^{2} \left (a \left (\cosh {\relax (x )} + 1\right )\right )^{\frac {3}{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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