∫ 4 cos (x + (π/6)) cos 2x . cos((5π/6) + x)dx

Question

∫ 4 cos (x + (π/6)) cos 2x . cos((5π/6) + x)dx  (A) -(x - ( sin4x/4) - ( sin2x/2)) +c  (B) -(x + ( sin4x/4) - ( sin2x/2)) +c  (C) -(x - ( sin4x/4) + ( sin2x/2)) +c  (D) -(x + ( sin4x/4) + ( sin2x/2)) +c

Tardigrade Admin · Accepted Answer

∫ 4 cos (x+(π/6)) cos 2 x ⋅ cos ((5 π/6)+π) d x =2 ∫( cos (2 x+π) cos (2 π/3)) cos 2 x d x =2 ∫(- cos 2 x-(1/2)) cos 2 x d x =∫(-2 cos 2 2 x- cos 2 x) d x =-∫(1+ cos 4 x+ cos 2 x) d x =-x-( sin 4 x/x)-( sin 2 x/2)+c

Q. $\int 4 cos (x + \frac{π}{6}) cos 2 x . cos (\frac{5 π}{6} + x) d x$

$- (x - \frac{s i n 4 x}{4} - \frac{s i n 2 x}{2}) + c$

$- (x + \frac{s i n 4 x}{4} - \frac{s i n 2 x}{2}) + c$

$- (x - \frac{s i n 4 x}{4} + \frac{s i n 2 x}{2}) + c$

$- (x + \frac{s i n 4 x}{4} + \frac{s i n 2 x}{2}) + c$

Q. ∫4cos(x+6π​)cos2x.cos(65π​+x)dx

−(x−4sin4x​−2sin2x​)+c

−(x+4sin4x​−2sin2x​)+c

−(x−4sin4x​+2sin2x​)+c

−(x+4sin4x​+2sin2x​)+c

∫4cos(x+6π​)cos2x⋅cos(65π​+π)dx =2∫(cos(2x+π)cos32π​)cos2xdx =2∫(−cos2x−21​)cos2xdx =∫(−2cos22x−cos2x)dx =−∫(1+cos4x+cos2x)dx =−x−xsin4x​−2sin2x​+c

Q. $\int 4 cos (x + \frac{π}{6}) cos 2 x . cos (\frac{5 π}{6} + x) d x$

$- (x - \frac{s i n 4 x}{4} - \frac{s i n 2 x}{2}) + c$

$- (x + \frac{s i n 4 x}{4} - \frac{s i n 2 x}{2}) + c$

$- (x - \frac{s i n 4 x}{4} + \frac{s i n 2 x}{2}) + c$

$- (x + \frac{s i n 4 x}{4} + \frac{s i n 2 x}{2}) + c$