\[ \int \cos (b x) \text {CosIntegral}(b x) \, dx \]
Optimal antiderivative \[ -\frac {\sinIntegral \! \left (2 b x \right )}{2 b}+\frac {\cosineIntegral \! \left (b x \right ) \sin \! \left (b x \right )}{b} \]
command
integrate(fresnel_cos(b*x)*cos(b*x),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
\[ \frac {\operatorname {Ci}\left (b x\right ) \sin \left (b x\right )}{b} - \frac {\Im \left ( \operatorname {Ci}\left (2 \, b x\right ) \right ) - \Im \left ( \operatorname {Ci}\left (-2 \, b x\right ) \right ) + 2 \, \operatorname {Si}\left (2 \, b x\right )}{4 \, b} \]