Question Number 5800 by sumit last updated on 28/May/16
$$\int\frac{{cos}\mathrm{2}{x}}{{sin}^{\mathrm{2}} {x}\centerdot{cos}^{\mathrm{2}} {x}}{dx} \\ $$$$ \\ $$
Commented by Boma last updated on 09/Aug/19
Boma
Answered by Yozzii last updated on 28/May/16
$$\int\frac{{cos}\mathrm{2}{x}}{{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}}{dx} \\ $$$$=\int\frac{{cos}\mathrm{2}{x}}{\left(\frac{{sin}\mathrm{2}{x}}{\mathrm{2}}\right)^{\mathrm{2}} }{dx} \\ $$$$=\mathrm{4}\int\frac{{cos}\mathrm{2}{x}}{{sin}^{\mathrm{2}} \mathrm{2}{x}}{dx} \\ $$$$=\mathrm{2}\int\frac{\mathrm{1}}{{u}^{\mathrm{2}} }{du}\:\:\:\:\:\:\left({u}={sin}\mathrm{2}{x}\right) \\ $$$$=−\frac{\mathrm{2}}{{u}}+{c} \\ $$$$\int\frac{{cos}\mathrm{2}{x}}{{sin}^{\mathrm{2}} {xcos}^{\mathrm{2}} {x}}{dx}={c}−\frac{\mathrm{2}}{{sin}\mathrm{2}{x}} \\ $$
Commented by Boma last updated on 09/Aug/19
Boma