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Question
Integrate the following with respect to x.
`(9x^2 - 4/x^2)^2`
Solution
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 x 1)) + "c"`
= `81/5 x^5 - 72x + 16(x^-3/13) + "c"`
= `81/5 x^5 - 72x - 16/3x^3 + "c"`
The number of non-zero rows = 3
∴ P(A) = 3
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