`int(dx)/(sqrt(1-e^(2x)))` is equal to

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

int(dx)/(sqrt(x-x^(2))) is equal to

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

int(dx)/(sqrt((1-x)(x-2))) is equal to

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

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(dx)/(sqrt(2e^(x)-1))=

int(1)/(sqrt(9x-4x^(2)))dx is equal to

int_(-1)^((1)/(2))(e^(x)(2-x^(2))dx)/((1-x)sqrt(1-x^(2))) is equal to (sqrt(e))/(2)(sqrt(3)+1) (b) (sqrt(3e))/(2)sqrt(3e)(d)sqrt((e)/(3))