The value of the integral `int_0^oo(xlogx)/((1+x^2)^2)dxi s` 0 (b) log 7 (c) 5 log 13 (d) none of these

The value of the definite integral int_0^(pi/2)(sin5x)/(sinx)dxi s 0 (b) pi/2 (c) pi (d) 2pi

lim_(x -> oo)(x(log(x)^3)/(1+x+x^2) equals 0 (b) -1 (c) 1 (d) none of these

The value of the integral int_(e^(-1))^(e^2)|((log)_e x)/x| dx is (A) 3/2 (B) 5/2 (C) 3 (D) 5

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

The value of int_1^e((tan^(-1)x)/x+(logx)/(1+x^2))dxi s tane (b) tan^(-1)e tan^(-1)(1/e) (d) none of these

The value of int_0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dxi s

The value of loga b-log|b|= (a) loga (b) "log"|a| (c) -loga (d) none of these

The value of int_0^1e^(x^2-x)dx is (a) 1 (c) > e^(-1/4) (d) none of these

The number of real solutions of the (log)_(0. 5)|x|=2|x| is (a) 1 (b) 2 (c) 0 (d) none of these