Question

`int(x + 1/x)^3 dx` = ______.

Options

• `1/4(x + 1/x)^4 + c`

• `x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c`

• `x^4/4 + (3x^2)/2 + 3log x + 1/x^2 + c`

• `(x - x^(-1))^3 + c`

Answer 1

`int(x + 1/x)^3 dx` = `bb(underline(x^4/4 + (3x^2)/2 + 3log x - 1/(2x^2) + c))`.

स्पष्टीकरण:

`(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3`

∴ `int(x + 1/x)^3dx = int(x^3 + 3x + 3/x + 1/x^3)dx`

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