2.2 Problem number 204

$$\int \frac{(e+fx{)}^2{\csc }^2(c+dx)}{a+a\sin (c+dx)}dx$$

Optimal antiderivative $$-\frac{2\mathrm{I}{(fx+e)}^2}{ad}+\frac{2{(fx+e)}^2\mathrm{arctanh}\left({\mathrm{e}}^{\mathrm{I}(dx+c)}\right)}{ad}-\frac{{(fx+e)}^2\cot (\frac{c}{2}+\frac{\pi }{4}+\frac{dx}{2})}{ad}-\frac{{(fx+e)}^2\cot (dx+c)}{ad}+\frac{4f(fx+e)\ln (1-\mathrm{I}{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^2}+\frac{2f(fx+e)\ln (1-{\mathrm{e}}^{2\mathrm{I}(dx+c)})}{a{d}^2}-\frac{2\mathrm{I}f(fx+e)\mathrm{polylog}(2,-{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^2}-\frac{4\mathrm{I}{f}^2\mathrm{polylog}(2,\mathrm{I}{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^3}+\frac{2\mathrm{I}f(fx+e)\mathrm{polylog}(2,{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^2}-\frac{\mathrm{I}{f}^2\mathrm{polylog}(2,{\mathrm{e}}^{2\mathrm{I}(dx+c)})}{a{d}^3}+\frac{2f^2\mathrm{polylog}(3,-{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^3}-\frac{2f^2\mathrm{polylog}(3,{\mathrm{e}}^{\mathrm{I}(dx+c)})}{a{d}^3}$$

command

integrate((f*x+e)^2*csc(d*x+c)^2/(a+a*sin(d*x+c)),x, algorithm="maxima")

Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output

$$\text{Exception raised: RuntimeError}$$

Maxima 5.44 via sagemath 9.3 output

$$\text{output too large to display}$$