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The integral int(3x^13+2x^11)/((2x^4+3x^...

The integral `int(3x^13+2x^11)/((2x^4+3x^2+1)^4)dx` is equal to (where C is a constant of integration)

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The correct Answer is:
6
`I = int(3x^(13)+2x^(11))/((2x^(4) + 3x^(2) + 1))dx = int((3x^(13) + 2x^(11)))/(x^(16)(2+(3)/(x^(2))+(1)/(x^(4)))^(4))dx = int((3x^(-3) + 2x^(-5))dx)/((2+3x^(-2)+x^(-4))^(4))`
Put `2 + 3x^(-2) + x^(-4) = t, (-6x^(-3) - 4x^(-5))dx = dt`
`(3x^(-3) + 2x^(-5))dx = -(dt)/(2), I = (-1)/(2)int(dt)/(t^(4)) = (1)/(6)(1)/(t^(3))+c , I = (x^(12))/(6(2x^(4)+3x^(2)+1)^(3))+c`
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