`int_0^oo(pi/(1+pi^2x^2)-1/(1+x^2))logxdx` is equal to (a)`-pi/2lnpi` (b) 0 (c)`pi/2ln2` (d) none of these

lim_(x->1)(1-x^2)/(sin2pix) is equal to (a) 1/(2pi) (b) -1/pi (c) (-2)/pi (d) none of these

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"

The value of integral int_0^(1/sqrt3) (dx)/((1+x^2)sqrt(1-x^2)) must be (a) 3+2pi (b) 4-pi (c) 2+pi (d) none of these

int_(-pi/2)^(pi/2)(e^(|sinx|)cosx)/(1+e^(tanx))dx is equal to (a) e+1 (b) 1-e (c) e-1 (d) none of these

(lim)_(xrarr0)(sin(picos^2x)/(x^2)) is equal to (a) -pi (b) pi (c) pi/2 (d) 1

G i v e nint_0^(pi/2)(dx)/(1+sinx+cosx)=log2. Then the value of integral int_0^(pi/2)(sinx)/(1+sinx+cosx)dx is equal to (a) 1/2log2 (b) pi/2-log2 (c) pi/4-1/2log2 (d) pi/2+log2

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to 0 (b) 2pi (c) pi (d) none of these

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

The value of int_(-pi//2)^(pi//2)(x^(2)cosx)/(1+e^(x)) d x is equal to

T h ev a l u eofint_1^((1+sqrt(5))/2)(x^2+1)/(x^4-x^2+1)log(1+x-1/x)dxi s (a) pi/8(log)_e2 (b) pi/2(log)_e2 (c) -pi/2(log)_e2 (d) none of these