Optimal. Leaf size=20 \[ \sin (a) \text {Si}\left (\frac {b}{x}\right )-\cos (a) \text {Ci}\left (\frac {b}{x}\right ) \]
[Out]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 20, 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 = {3378, 3376, 3375} \[ \sin (a) \text {Si}\left (\frac {b}{x}\right )-\cos (a) \text {CosIntegral}\left (\frac {b}{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 3375
Rule 3376
Rule 3378
Rubi steps
\begin {align*} \int \frac {\cos \left (a+\frac {b}{x}\right )}{x} \, dx &=\cos (a) \int \frac {\cos \left (\frac {b}{x}\right )}{x} \, dx-\sin (a) \int \frac {\sin \left (\frac {b}{x}\right )}{x} \, dx\\ &=-\cos (a) \text {Ci}\left (\frac {b}{x}\right )+\sin (a) \text {Si}\left (\frac {b}{x}\right )\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.04, size = 20, normalized size = 1.00 \[ \sin (a) \text {Si}\left (\frac {b}{x}\right )-\cos (a) \text {Ci}\left (\frac {b}{x}\right ) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.43, size = 28, normalized size = 1.40 \[ -\frac {1}{2} \, {\left (\operatorname {Ci}\left (\frac {b}{x}\right ) + \operatorname {Ci}\left (-\frac {b}{x}\right )\right )} \cos \relax (a) + \sin \relax (a) \operatorname {Si}\left (\frac {b}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [B] time = 0.41, size = 41, normalized size = 2.05 \[ -\frac {b \cos \relax (a) \operatorname {Ci}\left (-a + \frac {a x + b}{x}\right ) + b \sin \relax (a) \operatorname {Si}\left (a - \frac {a x + b}{x}\right )}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.04, size = 21, normalized size = 1.05 \[ -\Ci \left (\frac {b}{x}\right ) \cos \relax (a )+\Si \left (\frac {b}{x}\right ) \sin \relax (a ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [C] time = 2.01, size = 43, normalized size = 2.15 \[ -\frac {1}{2} \, {\left ({\rm Ei}\left (\frac {i \, b}{x}\right ) + {\rm Ei}\left (-\frac {i \, b}{x}\right )\right )} \cos \relax (a) - \frac {1}{2} \, {\left (i \, {\rm Ei}\left (\frac {i \, b}{x}\right ) - i \, {\rm Ei}\left (-\frac {i \, b}{x}\right )\right )} \sin \relax (a) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.05 \[ \sin \relax (a)\,\mathrm {sinint}\left (\frac {b}{x}\right )-\cos \relax (a)\,\mathrm {cosint}\left (\frac {b}{x}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.97, size = 15, normalized size = 0.75 \[ \sin {\relax (a )} \operatorname {Si}{\left (\frac {b}{x} \right )} - \cos {\relax (a )} \operatorname {Ci}{\left (\frac {b}{x} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________