Question

How do you find `\int e ^ { x } \sec ( e ^ { x } ) d x`?

Answer 1

`ln|sect+tant|.`

Explanation:

The substn. `e^x=t rArr e^xdx=dt.`

`:. inte^xsec(e^x)dx=intsec t dt`

`=ln|sect+tant|,`

`rArr inte^xsec(e^x)dx=ln|sece^x+tane^x|+C.`