int(4cos^(2)x-3sin^(2)x)/(sin^(2)2x)d(4x)

int(cos^(2)x)/(sin^(4)x)=

Solve the equation sin^(4)x+cos^(4)x-2sin^(2)x+(3sin^(2)2x)/(4)=0

4int(sin^(3)x+cos^(3)x)/(sin^(2)2x)dx=

4int(sin^(3)x+cos^(3)x)/(sin^(2)2x)dx=

int((sqrt(2sin2x+4cos^(2)x+sin4x)-2x)/(1+sin2x))dx

int(2cos2x)/(3+4sin2x)

Let Delta(x)=|(3+2sin^(4)x,2cos^(4)x,sin^(2)2x),(2sin^(4)x,3+2cos^(4)x,sin^(2)2x),(2sin^(4)x,2cos^(4)x,3+sin^(2)2x)| then int_(-pi//2)^(pi//2)x Delta(x)dx equals

int(a^(2)sin^(2)x+b^(2)cos^(2)x)/(a^(4)sin^(2)x+b^(4)cos^(2)x)dx

Prove : int (cos^(4)x)/(sin^(2)x) dx = - ( (3x)/2 + 1/4 sin2x + cot x ) + c