Question

Integrate the following with respect to x:

`(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)`

Answer 1

`int [(x + 4)^5 + 5/(2 - 5x)^4 - "cosec"^2 (3x - 1)] "d"x`

= `int (x + 4)^5 "d"x + 5 int 1/(2 - 5x)^4  "d"x - int  "cosec"^2(3x - 1)  "d"x`

= `(x + 4)^6/6 + (- 5)/(- 5 xx 3(2 - 5x)^3) + (cot(3x - 1))/3 + "c"`

= `(x + 4)^6/6 + 1/(3(2 - 5x)^3) + (cot(3x - 1))/3 + "c"`