`int(ln(1+e^(x))-x)/(1+e^(x))dx` equals:

int(ln(e^(x)+1))/(e^(x))dx

int sqrt((e^(x)-1)/(e^(x)+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 _( log 1//2 ) ^( log 2) sin { (e ^(x) -1)/( e ^(x ) +1 )}dx equals

int log(e^(x)+1)(e^(x))dx

int(e^(ln x))/(1+x^(2))dx

int ln((1)/(e^(x)))dx

The value of int_(log1//2)^(log2)sin{(e^(x)-1)/(e^(x)+1)}dx is equal to

int_(0)^(log 2)(e^(x))/(1+e^(x))dx=

int(e^(ln tan^(-1)x))/(1+x^(2))dx