Question

Integrate the following with respect to x.

`(9x^2 - 4/x^2)^2`

Answer 1

A = `[(-2, 1, 3, 4),(0, 1, 1, 2),(1, 3, 4, 7)]`

The order of A is 3 × 4

∴ P(A) < 3

Let us transform the matrix A to an echelon form

`int (9x^2 - 4/x^2)^2  "d"x`

= `int[(9x^2)^2 - 2(9x^2) (4/x^2) + (4/x^2)^2] "d"x`

= `int (81x^4 - 72 16/x^4)  "d"x`

= `int (81x^4 - 72 + 16x^-4)  "d"x`

= `(81x^5)/5 - 72x + 16((x^(-4+1))/(-4 + 1)) + "c"`

= `81/5 x^5 - 72x + 16(x^-3/3) + "c"`

= `81/5 x^5 - 72x - 16/3x^-3 + "c"`

The number of non-zero rows = 3

∴ P(A) = 3