Evaluate `cos(x/2)cos(x/2^2)sin(x/2^2)`

Find the maximum value of 4sin^(2)x+3cos^(2)x+sin((x)/(2))+cos((x)/(2))

Evaluate int(sin2x)/(a^2cos^2x+b^2sin^2x)dx

Simplify tan^(-1)((cos(x/2)+sin(x/2))/(cos(x/2)-sin(x/2)))

Evaluate: int(cos4x-cos2x)/(sin4x-sin2x)dx

Evaluate: int(cos x-sin x)/(cos x+sin x)(2+2sin2x)dx

Evaluate : (i) int(cos2x+2sin^(2)x)/(sin^(2)x)dx (ii) int(2cos^(2)x-cos2x)/(cos^(2)x)dx

If f(x)=|[cos(x +x^2), sin(x +x^2),-cos(x+x^2)],[ sin(x-x^2), cos(x -x^2), sin(x-x^2)],[sin2x,0,sin2x^2]| then find f'(x)

Evaluate: int(sin x cos x)/(3sin^(2)x-4cos^(2)x)dx

Evaluate :int(sin^(6)x+cos^(6)x)/(sin^(2)x*cos^(2)x)dx

Evaluate: int(sin x+2cos x)/(2sin x+cos x)dx