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int(pi/8)^(3 pi/8)(tan^(2)x)/(tan^(2)x+c...

int_(pi/8)^(3 pi/8)(tan^(2)x)/(tan^(2)x+cot^(2)x)dx=(pi)/(8)

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Prove that int_(pi/8)^(3 pi/8)(tan^(2)x backslash dx)/(tan^(2)x+cot^(2)x)=(pi)/(8)

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int_(0)^(pi//2) (tan^(7)x)/(cot^(7)x+ tan^(7)x)dx

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int_(0)^( pi)(x tan x)/(tan x+sec x)*dx=(pi(pi-2))/(2)