Optimal. Leaf size=16 \[ x \text{CosIntegral}(b x)-\frac{\sin (b x)}{b} \]
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Rubi [A] time = 0.0044011, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 4, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25, Rules used = {6500} \[ x \text{CosIntegral}(b x)-\frac{\sin (b x)}{b} \]
Antiderivative was successfully verified.
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Rule 6500
Rubi steps
\begin{align*} \int \text{Ci}(b x) \, dx &=x \text{Ci}(b x)-\frac{\sin (b x)}{b}\\ \end{align*}
Mathematica [A] time = 0.0014589, size = 16, normalized size = 1. \[ x \text{CosIntegral}(b x)-\frac{\sin (b x)}{b} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 19, normalized size = 1.2 \begin{align*}{\frac{bx{\it Ci} \left ( bx \right ) -\sin \left ( bx \right ) }{b}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [F] time = 0., size = 0, normalized size = 0. \begin{align*} \int{\rm Ci}\left (b x\right )\,{d x} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [F] time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\operatorname{Ci}\left (b x\right ), x\right ) \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] time = 1.68395, size = 31, normalized size = 1.94 \begin{align*} - x \log{\left (b x \right )} + \frac{x \log{\left (b^{2} x^{2} \right )}}{2} + x \operatorname{Ci}{\left (b x \right )} - \frac{\sin{\left (b x \right )}}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.19137, size = 22, normalized size = 1.38 \begin{align*} x \operatorname{Ci}\left (b x\right ) - \frac{\sin \left (b x\right )}{b} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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