Question Number 187251 by horsebrand11 last updated on 15/Feb/23
$$\:\:\int\:\frac{\mathrm{cos}\:\mathrm{9}{x}}{\mathrm{cos}\:\mathrm{4}{x}.\:\mathrm{cos}\:\mathrm{2}{x}}\:{dx}=? \\ $$
Commented by MJS_new last updated on 15/Feb/23
$$=\mathrm{4}\int\left(\mathrm{1}−\mathrm{4sin}^{\mathrm{2}} \:{x}\right)\mathrm{cos}\:{x}\:{dx}− \\ $$$$\:\:\:\:−\int\frac{\mathrm{cos}\:{x}}{\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:{x}}{dx}− \\ $$$$\:\:\:\:−\frac{\mathrm{1}}{\mathrm{4}}\int\frac{\left(\mathrm{1}−\mathrm{2sin}^{\mathrm{2}} \:{x}\right)\mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{4}} \:{x}\:−\mathrm{sin}^{\mathrm{2}} \:{x}\:+\mathrm{1}/\mathrm{8}}{dx} \\ $$$$\mathrm{and}\:\mathrm{these}\:\mathrm{are}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{solve} \\ $$