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 = 0.03, 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 \left ((a+b x)^2\right )}{x^2} \, dx \end {gather*}
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 \text {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 = 7.43, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh \left ((a+b x)^2\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.60, 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 \begin {gather*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [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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Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\cosh {\left (a^{2} + 2 a b x + b^{2} x^{2} \right )}}{x^{2}}\, 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 = -0.07 \begin {gather*} \int \frac {\mathrm {cosh}\left ({\left (a+b\,x\right )}^2\right )}{x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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