Question Number 45165 by Tinkutara last updated on 09/Oct/18
Answered by tanmay.chaudhury50@gmail.com last updated on 10/Oct/18
$$\int\frac{{sin}\mathrm{5}{x}\left(\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}.{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}{{sin}\mathrm{5}{x}−{sin}\mathrm{10}{x}}{dx} \\ $$$$\int\frac{\mathrm{2}{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}{cos}\frac{\mathrm{5}{x}}{\mathrm{2}}\left(\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}\right)}{−\mathrm{2}{cos}\frac{\mathrm{15}{x}}{\mathrm{2}}.{sin}\frac{\mathrm{5}{x}}{\mathrm{2}}}{dx} \\ $$$$=−\int\mathrm{2}{cos}\frac{\mathrm{5}{x}}{\mathrm{2}}.{cos}\frac{\mathrm{3}{x}}{\mathrm{2}}{dx} \\ $$$$=−\int{cos}\mathrm{4}{x}+{cosx}\:\:\:{dx} \\ $$$$=−\left(\frac{{sin}\mathrm{4}{x}}{\mathrm{4}}+{sinx}\right)+{c} \\ $$$${k}=\mathrm{4} \\ $$$$ \\ $$
Commented by Tinkutara last updated on 10/Oct/18
Thank you very much Sir! I got the answer. ��������
Commented by tanmay.chaudhury50@gmail.com last updated on 11/Oct/18
$${most}\:{welcome}... \\ $$