Question

Integrate the following with respect to x:

`sec^2  x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)`

Answer 1

`int [sec^2  x/5 + 18 cos2x + 10sec(5x + 3) tan(5x + 3)] "d"x`

= `int sec^2  x/5  "d"x + 18 int cos 2x  "d"x + 10 int  sec(5x + 3) tan(5x + 3)  "d"x`

= `(tan  x/5)/(1/5) + 18 ((sin 2x)/2) + 10 (sec(5x + 3))/5 + "c"`

= `5 tan  (x/5)/5 + 9 sin 2x + 2sec (5x + 3) + "c"`