int_(pi)^(0){cot^(-1)((2)/(2cos x-1))+cot^(-1)(cos x-(1)/(2))}dx=

int_(-(pi)/(3))^(0)[cot^(-1)((2)/(2cos x-1))+cot^(-1)(cos x-(1)/(2))]dx is equal to (pi^(2))/(6) (b) (pi^(2))/(3) (c) (pi^(2))/(8) (d) (3 pi^(2))/(8)

int_(0)^(10 pi)cot^(-1)(cos t)dx

int_(-2)^(3)[cot^(-1)((x-1)/(x+1))+cot^(-1)((x+1)/(x-1))]dx=

I=int_(0)^(2 pi)cos^(-1)(cos x)dx

int_(0)^(1)cot^(-1)(1-x+x^(2))dx

int_(0)^(1)cot^(-1)(1-x+x^(2))dx

int_(0)^(1)(cot^(-1)x)/(1+x^(2))dx

int_(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=

int_(-1)^(1)[tan^(-1){sin(cos^(-1)x)}+cot^(-1){cos(sin^(-1)x)}dx=