Optimal. Leaf size=21 \[ -\cosh (a) \text {Chi}\left (\frac {b}{x}\right )-\sinh (a) \text {Shi}\left (\frac {b}{x}\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {5319, 5317, 5316} \[ -\cosh (a) \text {Chi}\left (\frac {b}{x}\right )-\sinh (a) \text {Shi}\left (\frac {b}{x}\right ) \]
Antiderivative was successfully verified.
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Rule 5316
Rule 5317
Rule 5319
Rubi steps
\begin {align*} \int \frac {\cosh \left (a+\frac {b}{x}\right )}{x} \, dx &=\cosh (a) \int \frac {\cosh \left (\frac {b}{x}\right )}{x} \, dx+\sinh (a) \int \frac {\sinh \left (\frac {b}{x}\right )}{x} \, dx\\ &=-\cosh (a) \text {Chi}\left (\frac {b}{x}\right )-\sinh (a) \text {Shi}\left (\frac {b}{x}\right )\\ \end {align*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 1.00 \[ -\cosh (a) \text {Chi}\left (\frac {b}{x}\right )-\sinh (a) \text {Shi}\left (\frac {b}{x}\right ) \]
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 39, normalized size = 1.86 \[ -\frac {1}{2} \, {\left ({\rm Ei}\left (\frac {b}{x}\right ) + {\rm Ei}\left (-\frac {b}{x}\right )\right )} \cosh \relax (a) - \frac {1}{2} \, {\left ({\rm Ei}\left (\frac {b}{x}\right ) - {\rm Ei}\left (-\frac {b}{x}\right )\right )} \sinh \relax (a) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.14, size = 43, normalized size = 2.05 \[ -\frac {b {\rm Ei}\left (a - \frac {a x + b}{x}\right ) e^{\left (-a\right )} + b {\rm Ei}\left (-a + \frac {a x + b}{x}\right ) e^{a}}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 27, normalized size = 1.29 \[ \frac {{\mathrm e}^{-a} \Ei \left (1, \frac {b}{x}\right )}{2}+\frac {{\mathrm e}^{a} \Ei \left (1, -\frac {b}{x}\right )}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 24, normalized size = 1.14 \[ -\frac {1}{2} \, {\rm Ei}\left (-\frac {b}{x}\right ) e^{\left (-a\right )} - \frac {1}{2} \, {\rm Ei}\left (\frac {b}{x}\right ) e^{a} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ -\mathrm {cosh}\relax (a)\,\mathrm {coshint}\left (\frac {b}{x}\right )-\mathrm {sinh}\relax (a)\,\mathrm {sinhint}\left (\frac {b}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.08, size = 17, normalized size = 0.81 \[ - \sinh {\relax (a )} \operatorname {Shi}{\left (\frac {b}{x} \right )} - \cosh {\relax (a )} \operatorname {Chi}\left (\frac {b}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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