Question

`int ("e"^(7logx) - "e"^(6logx))/("e"^(5logx) - "e"^(4logx)) "d"x` = ______.

Options

• `x^3/3 + "c"`

• `1/x + "c"`

• `x^3log x + "c"`

• `3/x^3 + "c"`

Answer 1

`int ("e"^(lox) - "e"^(6logx))/("e"^(5logx) - "e"^(4logx)) "d"x` = `x^3/3 + "c"`.

Explanation:

`int ("e"^(7logx) - "e"^(6logx))/("e"^(5logx) - "e"^(4logx)) "d"x = int (x^7 - x^6)/(x^5 - x^4) "d"x`

= `int (x^6(x - 1))/(x^4(x - 1)) "d"x`

= `int x^2 "d"x`

= `x^3/3 + "c"`