`int_0^oo1/(1+e^x)dx` equals `log2-1` b. `log2` c. `log4-1` d. `log2`

int_0^oo1/(1+e^x)dx equals a. log2-1 b. log2 c. log4-1 d. log2

int_(0tooo) log(1+x^2)/(1+x^2) dx equals-(A) log2(B) -a log2(C) 1/2 log2(D) -A/2 log2

The value of int_0^1(8log(1+x))/(1+x^2)dx is a. pilog2 b. \ pi/8log2 c. \ pi/2log2 d. log2

int _(0) ^(pi//2) (cos x )/( 1 + sin x ) dx equals to a) log 2 b) 2 log 2 c) (log2) ^(2) d) 1/2 log 2

int_0^(pi//2)(cosx)/((2+sinx)(1+sinx))dx equals (a) log(2/3) (b) log(3/2) (c) log(3/4) (d) log(4/3)

int_(0)^(pi)log(1+cosx)dx=-pi(log2)

The value of int_0^1(8 log(1+x))/(1+x^(2)) dx is a) πlog2 b) π/8log2 c) π/2log2 d) log2

int_(pi//6)^(pi//3)1/(sin2x)dx\ is equal to (log)_e3 b. (log)_"e"sqrt(3) c. 1/2log(-1) d. log(-1)

Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0. Then y '(1) equals: a. 1 b. log2 c. -log2 d. -1