`intsec^(3)xdx=?`

Options

A. `(1)/(2){secxtanx-log|secx+tanx|}+C`
B. `(1)/(2){secxtanx+log|secx+tanx|}+C`
C. `2{secxtanx+log|secx+tanx|}+C`
D. none of these

Answer

B

Explanation

`I=intunderset(II)(sec^(2))x*underset(I)(sec)xdx=secxtanx-intsecxtan^(2)xdx`
`=secxtanx-intsecx(sec^(2)x-1)dx=secxtanx-I+int+secxdx`
`:." "2I=secxtanx+log|secx+tanx|+C`.