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int(0)^( pi/6)(cos x)/(3+4sin x)dx...

`int_(0)^( pi/6)(cos x)/(3+4sin x)dx`

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int_(0)^( pi/3)(cos x)/(3+4sin x)dx

int_(0)^(pi//2)(cos x)/((3+sin x)(4+sin x))dx=

Prove that: int_(0)^( pi/2)(sin x)/(sin x-cos x)dx=(pi)/(4)

The value of the integral int_(0)^(pi/2)(cos x)/((2+sin x)(4+sin x))dx equals

u,=int_(0)^((pi)/(2))cos((2 pi)/(3)sin^(2)x)dx and v,=int_(0)^((pi)/(2))cos((pi)/(3)sin x)dx

int_(0)^((pi)/(2))((cos x)/(6-5sin x+sin^(2)x))dx

int_(0)^(pi)(cos^(4)x-sin^(4)x)dx=

int_(0)^(pi//6) cos x cos 3x dx

solve int_(0)^( pi/3)(4sin x)/(cos^(2)x)dx

int_(0)^(pi//2)(cos^(4)x)/((sin^(4)x+cos^(4)x))dx=(pi)/(4)