Optimal. Leaf size=14 \[ \text{Unintegrable}\left (\frac{\cosh \left ((a+b x)^2\right )}{x^2},x\right ) \]
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Rubi [A] time = 0.0402896, 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 = {} \[ \int \frac{\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin{align*} \int \frac{\cosh \left ((a+b x)^2\right )}{x^2} \, dx &=b \operatorname{Subst}\left (\int \frac{\cosh \left (x^2\right )}{(-a+x)^2} \, dx,x,a+b x\right )\\ \end{align*}
Mathematica [A] time = 10.1968, size = 0, normalized size = 0. \[ \int \frac{\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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Maple [A] time = 0.047, size = 0, normalized size = 0. \begin{align*} \int{\frac{\cosh \left ( \left ( bx+a \right ) ^{2} \right ) }{{x}^{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{\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{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{\cosh \left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{x^{2}}, 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{\cosh{\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{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{\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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