Optimal. Leaf size=61 \[ -\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;-i b x)+\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;i b x)+\frac {1}{2} \log ^2(b x)+\gamma \log (x) \]
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Rubi [A] time = 0.02, antiderivative size = 61, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {6502} \[ -\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;-i b x)+\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;i b x)+\frac {1}{2} \log ^2(b x)+\gamma \log (x) \]
Antiderivative was successfully verified.
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Rule 6502
Rubi steps
\begin {align*} \int \frac {\text {Ci}(b x)}{x} \, dx &=-\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;-i b x)+\frac {1}{2} i b x \, _3F_3(1,1,1;2,2,2;i b x)+\gamma \log (x)+\frac {1}{2} \log ^2(b x)\\ \end {align*}
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Mathematica [A] time = 0.05, size = 94, normalized size = 1.54 \[ \frac {1}{2} \left (-i b x \, _3F_3(1,1,1;2,2,2;-i b x)+i b x \, _3F_3(1,1,1;2,2,2;i b x)+\log (x) (2 \text {Ci}(b x)+\log (-i b x)+\log (i b x)+\Gamma (0,-i b x)+\Gamma (0,i b x)-\log (x)+2 \gamma )\right ) \]
Antiderivative was successfully verified.
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fricas [F] time = 0.99, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {\operatorname {Ci}\left (b x\right )}{x}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\rm Ci}\left (b x\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 158, normalized size = 2.59 \[ \frac {\sqrt {\pi }\, \left (-\frac {b^{2} x^{2} \hypergeom \left (\left [1, 1, 1\right ], \left [\frac {3}{2}, 2, 2, 2\right ], -\frac {b^{2} x^{2}}{4}\right )}{2 \sqrt {\pi }}+\frac {4 \ln \relax (x )^{2}+4 \ln \relax (2)^{2}+4 \ln \relax (b )^{2}-\frac {\pi ^{2}}{3}-4 \ln \relax (x ) \left (-\gamma -2 \ln \relax (2)\right )+4 \ln \relax (2) \left (-\gamma -2 \ln \relax (2)\right )-4 \ln \relax (b ) \left (-\gamma -2 \ln \relax (2)\right )-2 \gamma \left (-\gamma -2 \ln \relax (2)\right )-4 \ln \relax (2) \gamma +4 \ln \relax (x ) \gamma +\gamma ^{2}+4 \ln \relax (b ) \gamma -8 \ln \relax (x ) \ln \relax (2)+8 \ln \relax (x ) \ln \relax (b )-8 \ln \relax (2) \ln \relax (b )+\left (-\gamma -2 \ln \relax (2)\right )^{2}}{2 \sqrt {\pi }}\right )}{4} \]
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 \[ \int \frac {{\rm Ci}\left (b x\right )}{x}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.02 \[ \int \frac {\mathrm {cosint}\left (b\,x\right )}{x} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Exception raised: AttributeError} \]
Verification of antiderivative is not currently implemented for this CAS.
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