`int_2^4 log[x]dx` is (A) `log2` (B) `log3` (C) `log5` (D) none of these

The value of int_0^([x]) 2^x/2^([x])dx , where [x] denotes the greatest integer function is (A) [x]log2 (B) [x]/log2 (C) 1/2[x]/log2 (D) none of these

The value of int_0^(log5) (e^xsqrt(e^x-1))/(e^x+3)dx is (A) 3+2pi (B) 4-pi (C) 2+pi (D) none of these

int_(0)^(a)log(cot a+tan x)dx where a in(0,(pi)/(2)) is (A) a ln sin a(B)-a ln sin a(C)-a ln cos a (D) none of these

int_(log(1/2))^(log2) log(x+sqrt(x^2+1))dx= (A) 2log2 (B) 1-log2 (C) 1+log2 (D) 0

Largest integral value satisfying log_(x)2log_(2x)2log_(2)4x>1 is (A)4(B)3(C)2 (D) None of these

The value of the integral int_(0)^(oo)(x log x)/((1+x^(2))^(2))dx is 0(b)log7(c)5log13(d) none of these

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

int_0^1 log(sqrt(1+x)+sqrt(1-x))dx= (A) 1/2(log2-pi/2+1) (B) 1/2(log2+pi/2+1) (C) 1/2(log2+pi/2-1) (D) none of these

If y=(log)_(sin x)(tan x),then(((dy)/(dx)))_((pi)/(4)) is equal to (a) (4)/(log2)(b)-4log2(c)(-4)/(log2)(d) none of these

int(log_e(x+1)-log_ex)/(x(x+1))dx is equal to (A) -1/2[log(x+1)^2-1/2logx]^2+log_e(x+1)log_ex+C (B) -[(log_e(x+1)-log_ex]^2 (C) c-1/2(log(1+1/x))^2 (D) none of these