integratation of power of sines and cosines:

∫ sin^4 xcos^2xdx

Question

integratation of power of sines and cosines:

∫ sin^4 xcos^2xdx

anonymous · Answer

this is calculus

anonymous · Answer

$$-\frac{ \cos ^{5}x }{ 5 }+\frac{ \cos ^{7}x }{ 7 }+c$$

anonymous · Answer

how come? what case did you used? is it case 2?

anonymous · Answer

bak reyiz, cos^2 x=1-sin^2 x. biliyon mu bunu??

anonymous · Answer

what? im sorry i cant understant your language, could you speak in english please?

anonymous · Answer

can someone please help me? :(

callisto · Answer

I think it's not like what marsss did there...
$$∫ sin^4 xcos^2xdx$$$$=∫ sin^4 x(1-sin^2x)dx$$$$=∫ sin^4x-sin^6xdx$$$$=∫ (sin^2x)^2dx-∫(sin^2x)^3dx$$$$=\frac{1}{4}∫ (1-cos2x)^2dx-\frac{1}{8}∫(1-cos2x)^3dx$$$$=\frac{1}{4}∫ (1-2cos2x+cos^22x)dx-\frac{1}{8}∫(1-3cos2x+3cos^22x-cos^32x)dx$$
Reduce the power of cosine into 1 using doucle angle formula, except for cos^3(2x). Good luck :|