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Question
Find : `int (2x^2 + 3)/(x^2(x^2 + 9))dx; x ≠ 0`.
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Solution
We have, `(2x^2 + 3)/(x^2(x^2 + 9))`
Now, let x2 = t
So, `(2t + 3)/(t(t + 9)) = A/t + B/(t + 9)`, we get A = `1/3` and B = `5/3`
`int (2x^2 + 3)/(x^2(x^2 + 9))dx = 1/3 int dx/x^2 + 5/3 int dx/(x^2 + 9)`
= `-1/(3x) + 5/9 tan^-1 (x/3) + c`, where 'c' is an arbitrary constant of integration.
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