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If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(...

If `f(x)=int(3x^2+1)/((x^2-1)^3)dx` and `f(0)=0,` then the value of `|2/(f(2))|` is___

Text Solution

Verified by Experts

The correct Answer is:
-9
` f(x)=int(3x^(2)+1)/((x^(2)-1)^(3))dx`
`=int(-(x^(2)-1))/((x^(2)-1)^(3))dx+int(4x^(2))/((x^(2)-1)^(3))dx`
`=int[(-1)/((x^(2)-1)^(2))+x*(4x)/((x^(2)-1)^(3))]dx`
`=-int(dx)/((x^(2)-1)^(2))+x int(4xdx)/((x^(2)-1)^(3))-int((x)' int(4x)/((x^(2)-1)^(3))dx)dx`
`=x((-1)/((x^(2)-1)^(2)))+C`
`=-(x)/((x^(2)-1)^(2))+C`
`f(0)=0 implies C=0`
` :. f(x)=-(x)/((x^(2)-1)^(2))`
`"Now, " f(2)=-(2)/(9)`
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