\[ \int \frac {\text {CosIntegral}(a+b x)}{x^3} \, dx \]
Optimal antiderivative \[ \frac {b^{2} \cosineIntegral \! \left (b x +a \right )}{2 a^{2}}-\frac {\cosineIntegral \! \left (b x +a \right )}{2 x^{2}}-\frac {b^{2} \cosineIntegral \! \left (b x \right ) \cos \! \left (a \right )}{2 a^{2}}-\frac {b \cos \! \left (b x +a \right )}{2 a x}-\frac {b^{2} \cos \! \left (a \right ) \sinIntegral \! \left (b x \right )}{2 a}-\frac {b^{2} \cosineIntegral \! \left (b x \right ) \sin \! \left (a \right )}{2 a}+\frac {b^{2} \sinIntegral \! \left (b x \right ) \sin \! \left (a \right )}{2 a^{2}} \]
command
integrate(fresnel_cos(b*x+a)/x^3,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {output too large to display} \]