Question

Integrate the following functions with respect to x:

`1/(2 - 3x)^4`

Answer 1

`int ("a"x + "b")^"n"  "d"x = 1/"a" ("a"x + "b")^("n" + 1)/("n" + 1) + "c"`

`int 1/(2 - 3x)^4  "d"x = int  (2 - 3x)^-4 * "d"x`

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

= `1/(-3) (2 - 3x)^-3/(-3) + "c"`

= `1/9 xx 1/(2 - 3x)^3 + "c"`

= `1/(9(2 - 3x)^3 + "c"`