`int_0^oo(x dx)/((1+x)(1+x^2))` is equal to (A) `pi/4` (B) `pi/2` (C) `pi` (D) none of these"

int_0^1d/(dx){sin^(-1)((2x)/(1+x^2))}dx is equal to 0 (b) pi (c) pi//2 (d) pi//4

int_0^pi cos2xlogsinxdx= (A) pi (B) -pi/2 (C) pi/2 (D) none of these

int_0^pi dx/(1-2acosx+a^2), alt1 is equal to (A) (pialog2)/4 (B) (4pi)/(2-a^2) (C) pi/(1-a^2) (D) none of these

int_1^(e^(17))(pi"sin"(pi(log)_e x))/x dx is equal to (A) 2 (B) -2 (C) 2//pi (D) none of these

If n=2m+1,m in N uu{0}, then int_(0)^((pi)/(2))(sin nx)/(sin x)dx is equal to (i)pi(ii)(pi)/(2)(iii)(pi)/(4) (iv) none of these

int_0^oo logx/(1+x^2)dx= (A) log2 (B) pi/2 (C) 0 (D) none of these

("lim")_(xvecoo)"{"x+5")"tan^(-1)(x+5)-(x+1)tan^(-1)(x+1)} is equal to pi (b) 2pi (c) pi/2 (d) none of these

int_0^pi dx/(1+10^(cosx))+int_(-1)^1 log((2-x)/(2+x))dx= (A) pi/2 (B) -pi (C) 0 (D) none of these

If int_(pi/4)^((3pi)/4) x/(1+sinx)dx=k(sqrt(2)-1) , then k = (A) 0 (B) pi (C) 2pi (D) none of these