`int_0^oo (xlogx)/(1+x^2)^2dx=` (A) `e` (B) `1` (C) `0` (D) none of these

int_0^oo logx/(1+x^2)dx= (A) log2 (B) pi/2 (C) 0 (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

int_0^pi sqrt((1+cos2x)/2)dx= (A) 0 (B) 1 (C) 2 (D) none of these

int_(0)^(oo)(x logx)/((1+x^(2))^(2)) dx=

sqrt(3)int_0^pi dx/(1+2sin^2x)= (A) -pi (B) 0 (C) pi (D) none of these

If n in N and int_0^1 e^x(x-1)^ndx=2e-5 , then n= (A) 1 (B) 2 (C) 3 (D) none of these

int_0^pi (sin((n+1)/2)x)/sinxdx= (A) 0 (B) pi/2 (C) pi (D) none of these

If int_0^1 xe^(x^2) dx=k int_0^1 e^(x^2) dx , then (A) kgt1 (B) 0ltklt1 (C) k=1 (D) none of these

int[1/logx-1/(logx)^2]dx= (A) x/logx (B) xlogx (C) logx/x (D) none of these

Let f(x) be a continuous function such that f(a-x)+f(x)=0 for all x in [0,a] . Then int_0^a dx/(1+e^(f(x)))= (A) a (B) a/2 (C) 1/2f(a) (D) none of these