Integrand size = 12, antiderivative size = 12 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\text {Int}\left (\frac {\cosh \left ((a+b x)^2\right )}{x^2},x\right ) \]
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Not integrable
Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = b \text {Subst}\left (\int \frac {\cosh \left (x^2\right )}{(-a+x)^2} \, dx,x,a+b x\right ) \\ \end{align*}
Not integrable
Time = 3.36 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \]
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Not integrable
Time = 0.02 (sec) , antiderivative size = 12, normalized size of antiderivative = 1.00
\[\int \frac {\cosh \left (\left (b x +a \right )^{2}\right )}{x^{2}}d x\]
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Not integrable
Time = 0.25 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.92 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int { \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 3.04 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.83 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int \frac {\cosh {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{2}}\, dx \]
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Not integrable
Time = 0.61 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int { \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int { \frac {\cosh \left ({\left (b x + a\right )}^{2}\right )}{x^{2}} \,d x } \]
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Not integrable
Time = 1.57 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.17 \[ \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx=\int \frac {\mathrm {cosh}\left ({\left (a+b\,x\right )}^2\right )}{x^2} \,d x \]
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