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int(0)^((pi)/(2))(cos^(5)xdx)/(sin^(5)x+...

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

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By using the properties of definite integrals, evaluate the integrals int_(0)^((pi)/(2))(cos^(5)xdx)/(sin^(5)+cos^(5)x)

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

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

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

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

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

(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4) (ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)