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

int_(1)^(3)|(2-x)log_(e )x|dx is equal to:

inte^(3 log x ) (x^(4)+ 1) ^(-1) dx is equal to

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)

If int(2^(1setminusx))/(x^2)\ dx=k\ 2^(1setminusx)+C , then k is equal to -1/((log)_e2) (b) (log)_e2 (c) -1 (d) 1/2

int( (log x)^(5) )/( x ) dx is equal to a) (log x^(6))/( 6) + C b) ( ( log x )^(6))/( 6) + C c) ((log x )^(6))/( 3x^(2)) + C d) none of these

int_(1//3)^(3)(1)/(x)log_(e)(|(x+x^(2)-1)/(x-x^(2)+1)|)dx is equal to

Column I, a) int(e^(2x)-1)/(e^(2x)+1)dx is equal to b) int1/((e^x+e^(-x))^2)dx is equal to c) int(e^(-x))/(1+e^x)dx is equal to d) int1/(sqrt(1-e^(2x)))dx is equal to COLUMN II p) x-log[1+sqrt(1-e^(2x)]+c q) log(e^x+1)-x-e^(-x)+c r) log(e^(2x)+1)-x+c s) -1/(2(e^(2x)+1))+c

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

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

int_(1//e)^(e) (dx)/(x(log x)^(1//3))