\[ \int \cos (5 x) \text {CosIntegral}(2 x) \, dx \]
Optimal antiderivative \[ -\frac {\sinIntegral \! \left (3 x \right )}{10}-\frac {\sinIntegral \! \left (7 x \right )}{10}+\frac {\cosineIntegral \! \left (2 x \right ) \sin \! \left (5 x \right )}{5} \]
command
integrate(fresnel_cos(2*x)*cos(5*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
\[ \frac {1}{5} \, \operatorname {Ci}\left (2 \, x\right ) \sin \left (5 \, x\right ) - \frac {1}{10} \, \operatorname {Si}\left (7 \, x\right ) - \frac {1}{10} \, \operatorname {Si}\left (3 \, x\right ) \]