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int(0)^((pi)/(4))(sin x+cos x)/(3+sin2x)...

int_(0)^((pi)/(4))(sin x+cos x)/(3+sin2x)dx

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The value of the integral int_0^(pi/4) (sin x + cos x)/(3 + sin 2x) dx is equal to

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

int_0^(pi//4) (sin x + cos x)/(3 + sin 2x ) dx =

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

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