Question

What is the integral of `(secxtanx)(1+secx)dx`?

Answer 1

`1/2 (1+secx)^2+C`

`int (secxtanx)(1+secx)dx=int (1+secx)(secxtanx)dx`

Let `u=1+secx`. Then `du=secxtanxdx`

`int udu=1/2u^2+C` So,

`int (secxtanx)(1+secx)dx=1/2(1+secx)^2+C`