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

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

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

Evaluate: (i) int(e^(x)+1)/(e^(x)+x)dx( ii) int(1)/(x log x)dx

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

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

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

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

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