`I=int(e^(x))/(e^(4x)+1)dx`

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

I=int(e^(2x)-1)/(e^(2x))dx

int(3e^(x)-4)/(e^(x)+1)dx=

int(e^(4x)-1)/(e^(2x))dx

int(e^(-x))/(1+e^(x))dx=

I=int(e^x)/(e^(x)-1)dx

Let I =int(e^(x))/(e^(4x)+e^(2x)+1)dx , J = int(e^(-x))/(e^(-4x)+e^(-2x)+1)dx . Then for an arbitary constant C, the value of I - J equals

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(e^(4x)-e^(-4x))dx

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