38.17 Problem number 265

\[ \int \frac {(e+f x) \cos ^3(c+d x)}{a+a \sin (c+d x)} \, dx \]

Optimal antiderivative \[ \frac {f x}{4 a d}+\frac {f \cos \left (d x +c \right )}{a \,d^{2}}+\frac {\left (f x +e \right ) \sin \left (d x +c \right )}{a d}-\frac {f \cos \left (d x +c \right ) \sin \left (d x +c \right )}{4 a \,d^{2}}-\frac {\left (f x +e \right ) \left (\sin ^{2}\left (d x +c \right )\right )}{2 a d} \]

command

integrate((f*x+e)*cos(d*x+c)^3/(a+a*sin(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 \[ \text {Timed out} \]_______________________________________________________