Evaluate
`int_(0)^(pi)sqrt((cosx+cos2x+cos3x)^(2)+(sinx+sin2x+sin3x)^(2))dx`

int_(0)^( pi)sqrt((cos x+cos2x+cos3x)^(2)+(sin x+sin2x+sin3x)^(2))dx is equal to ((pi)/(k)+w), where k and w are positive integers,find the value of (k^(2)+w^(2))

Evaluate : int_(0)^(pi/2)(sin^2x-cos^2x)/(sin^3x+cos^3x)dx

Evaluate :int_(0)^( pi/4)cos2x sqrt(4-sin2x)dx

Evaluate: int_(0)^( pi/2)(1)/(cos^(3)x sqrt(2sin2x))dx

int_(0)^((pi)/2)(cos2x)/(cosx+sinx)dx=

int_(0)^((pi)/2)(cos2x)/(cosx+sinx)dx=

Evaluate : int_(pi/3)^( pi/3)(sin x+cos x)/(sqrt(sin2x))dx

Evaluate : (i) int_(0)^(pi//2)(cosx)/((cos\ (x)/(2)+sin\ (x)/(2)))dx (ii) int_(0)^(pi//2)(cosx)/((1+cosx+sinx))dx

Evaluate: int(dx)/(cos^(3)x sqrt(sin2x))