Question

Integrate the following with respect to x:

`8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)`

Answer 1

`int [8/sqrt(1 - (4x)^2) + 27/sqrt(1 - 9x^2) - 15/(1 + 25x^2)]  "d"x`

= `8 int 1/sqrt(1 - (4x)^2)  "d"x + 24int  1/sqrt(1 - (3x)^2)  "d"x - 15int 1/sqrt(1 + (5x)^2)  "d"x`

= `8/4 sin^-1 (4x) + 27/3 sin^-1 (3x) (- 15)/5  tan^-1 (5x) + "c"`

= `2sin^-1 (4x) + 9sin^-1 (3x) - 3tan^-1(5x) + "c"`