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int(0)^( pi)(dx)/(1-2a cos x+a^(2)),a>1...

int_(0)^( pi)(dx)/(1-2a cos x+a^(2)),a>1

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For 0 lt alt 1 ,the value of the integral int_(0)^( pi)(dx)/(1-2a cos x+a^(2)) is:

int_(0)^( pi)(dx)/(1+cos x)

int_(0)^(pi//2) (dx)/(1+2 cos x)

int_(0)^( pi)(dx)/(1+cos^(2)x)

int_(0)^(pi/2)(x)/(1+cos x)dx =

int_(0)^(pi) (1)/(5+2 cos x)dx

int_(0)^(pi) (1)/(5+2 cos x)dx

int_(0)^((pi)/(2))(dx)/(1+2cos x)

int_(0)^(pi/2)(1)/(6-cos x)dx

int_(0)^(pi//2)(dx)/((1+cos^(2)x))