ज्ञात करें `int (dx)/(e^x + e^(-x))`

Explanation

`int = (dx)/(e^x+e^(-1))=int (dx)/(e^x+1/e^x)=int e^x/(e^(2x)+1)dx = int e^x/(1+(e^x)^2)dx" ...(1)"`
माना की `e^x = tan theta,` तो ` e^x dx = sec^2 theta d theta`
अब (1) से, `int (dx)/(e^x +e^(-x))=int e^x/(1+(e^x)^2)dx=int (sec^2 theta)/(1+tan^2 theta) d theta = int d theta = theta +c `
`= tan^(-1)(e^(x))+c" "[ because tan theta = e^x = tan^(-1)(e^(x))]`