41.6 Problem number 76

\[ \int \frac {\text {CosIntegral}(b x)}{x^3} \, dx \]

Optimal antiderivative \[ -\frac {b^{2} \cosineIntegral \! \left (b x \right )}{4}-\frac {\cosineIntegral \! \left (b x \right )}{2 x^{2}}-\frac {\cos \! \left (b x \right )}{4 x^{2}}+\frac {b \sin \! \left (b x \right )}{4 x} \]

command

integrate(fresnel_cos(b*x)/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

\[ -\frac {b^{2} x^{2} \operatorname {Ci}\left (b x\right ) + b^{2} x^{2} \operatorname {Ci}\left (-b x\right ) - 2 \, b x \sin \left (b x\right ) + 2 \, \cos \left (b x\right )}{8 \, x^{2}} - \frac {\operatorname {Ci}\left (b x\right )}{2 \, x^{2}} \]