Evaluate: `inte^xsecx\ (1+tanx)\ dx`

Answer

b

Explanation

`" Let " I= int e^(x) sec x(1+tanx) dx`
`rArr I= int e^(x) sec x dx + int e^(x) sec x tan x dx " " .....(1)`
`" Now " int e^(x) sec x dx`
` = sec x int e^(x) dx- int ((d)/(dx) sec x int e^(x) dx)dx`
` =e^(x) sec x- int sec x tan x e^(x) dx" " .....(2)`
Put the value from equation (2) to equation (1)
` I=e^(x) sec x- int e^(x) sec x tan xdx`
`+ int sec x tan xe^(x) dx+C`
`rArr I=e^(x) sec x+C`