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int(0)^((pi)/(2))(dx)/(5+4sin x)...

int_(0)^((pi)/(2))(dx)/(5+4sin x)

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Evaluate the following : int_(0)^((pi)/(2)) (dx)/( 5+4 sin^(2) x )

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

int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

int_(0)^(pi//2) (dx)/(4sin^(2) x + 5 cos^(2)x)

int_(0)^(pi//2)(1)/(5+13 sin x) dx=

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

int_ (0) ^ ((pi) / (2)) (sin x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (cos x) / (sin x + cos x) dx = int_ (0) ^ ((pi) / (2)) (dx) / (1 + cot x) = int_ (0) ^ ((pi) / (2)) (dx) / ( 1 + time x) = (pi) / (4)

Evaluate: int_(0)^(pi/2)(dx)/(4sin^(2)x+5cos^(2)x)