Optimal. Leaf size=15 \[ \text {Int}\left (\frac {\cosh \left ((a+b x)^2\right )}{x^2},x\right ) \]
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Rubi [A] time = 0.04, 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 = {} \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
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*}
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Mathematica [A] time = 11.05, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.66, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\cosh \left (b^{2} x^{2} + 2 \, a b x + a^{2}\right )}{x^{2}}, x\right ) \]
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 \[ \int \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.16, size = 0, normalized size = 0.00 \[ \int \frac {\cosh \left (\left (b x +a \right )^{2}\right )}{x^{2}}\, dx \]
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 \[ \int \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.07 \[ \int \frac {\mathrm {cosh}\left ({\left (a+b\,x\right )}^2\right )}{x^2} \,d x \]
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 \[ \int \frac {\cosh {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{2}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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