\[ \int x \cos (a+b x) \text {Si}(c+d x) \, dx \]
Optimal antiderivative \[ \frac {c \cosineIntegral \left (\frac {c \left (b -d \right )}{d}+\left (b -d \right ) x \right ) \cos \left (a -\frac {b c}{d}\right )}{2 b d}-\frac {c \cosineIntegral \left (\frac {c \left (b +d \right )}{d}+\left (b +d \right ) x \right ) \cos \left (a -\frac {b c}{d}\right )}{2 b d}+\frac {\cos \left (a -\frac {b c}{d}\right ) \sinIntegral \left (\frac {c \left (b -d \right )}{d}+\left (b -d \right ) x \right )}{2 b^{2}}+\frac {\cos \left (b x +a \right ) \sinIntegral \left (d x +c \right )}{b^{2}}-\frac {\cos \left (a -\frac {b c}{d}\right ) \sinIntegral \left (\frac {c \left (b +d \right )}{d}+\left (b +d \right ) x \right )}{2 b^{2}}+\frac {\cosineIntegral \left (\frac {c \left (b -d \right )}{d}+\left (b -d \right ) x \right ) \sin \left (a -\frac {b c}{d}\right )}{2 b^{2}}-\frac {\cosineIntegral \left (\frac {c \left (b +d \right )}{d}+\left (b +d \right ) x \right ) \sin \left (a -\frac {b c}{d}\right )}{2 b^{2}}-\frac {c \sinIntegral \left (\frac {c \left (b -d \right )}{d}+\left (b -d \right ) x \right ) \sin \left (a -\frac {b c}{d}\right )}{2 b d}+\frac {c \sinIntegral \left (\frac {c \left (b +d \right )}{d}+\left (b +d \right ) x \right ) \sin \left (a -\frac {b c}{d}\right )}{2 b d}+\frac {x \sinIntegral \left (d x +c \right ) \sin \left (b x +a \right )}{b}-\frac {\sin \left (a -c +\left (b -d \right ) x \right )}{2 b \left (b -d \right )}+\frac {\sin \left (a +c +\left (b +d \right ) x \right )}{2 b \left (b +d \right )} \]
command
integrate(x*cos(b*x+a)*sin_integral(d*x+c),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {output too large to display} \]
Giac 1.7.0 via sagemath 9.3 output \[ \text {Timed out} \]_______________________________________________________