Optimal. Leaf size=27 \[ \frac {(a+b x) \text {Ci}(a+b x)}{b}-\frac {\sin (a+b x)}{b} \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6500} \[ \frac {(a+b x) \text {CosIntegral}(a+b x)}{b}-\frac {\sin (a+b x)}{b} \]
Antiderivative was successfully verified.
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Rule 6500
Rubi steps
\begin {align*} \int \text {Ci}(a+b x) \, dx &=\frac {(a+b x) \text {Ci}(a+b x)}{b}-\frac {\sin (a+b x)}{b}\\ \end {align*}
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Mathematica [A] time = 0.04, size = 42, normalized size = 1.56 \[ x \text {Ci}(a+b x)+\frac {a \text {Ci}(a+b x)}{b}-\frac {\sin (a) \cos (b x)}{b}-\frac {\cos (a) \sin (b x)}{b} \]
Antiderivative was successfully verified.
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fricas [F] time = 1.00, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\operatorname {Ci}\left (b x + a\right ), x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.21, size = 85, normalized size = 3.15 \[ x \operatorname {Ci}\left (b x + a\right ) + \frac {a \cos \relax (a)^{2} \operatorname {Ci}\left (b x + a\right ) + a \cos \relax (a)^{2} \operatorname {Ci}\left (-b x - a\right ) + a \operatorname {Ci}\left (b x + a\right ) \sin \relax (a)^{2} + a \operatorname {Ci}\left (-b x - a\right ) \sin \relax (a)^{2} - 2 \, \cos \relax (a) \sin \left (b x\right ) - 2 \, \cos \left (b x\right ) \sin \relax (a)}{2 \, b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 26, normalized size = 0.96 \[ \frac {\left (b x +a \right ) \Ci \left (b x +a \right )-\sin \left (b x +a \right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int {\rm Ci}\left (b x + a\right )\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \[ x\,\mathrm {cosint}\left (a+b\,x\right )-\frac {\sin \left (a+b\,x\right )-a\,\mathrm {cosint}\left (a+b\,x\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \operatorname {Ci}{\left (a + b x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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