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Evaluate: `Int (2y^2)/(Y^2 + 4)Dx` - Mathematics

Evaluate: `int (2y^2)/(y^2 + 4)dx`

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Solution

`I = int (2y^2)/(y^2 + 4) dy`

`= int(2y^2 + 8 - 8)/(y^2 + 4) dy`

`= 2int (y^2 + 4)/(y^2 + 4) dy - 8 int dy/(y^2 + 2^2)`

`= 2y - 4tan^(-1) (y/2) + c`

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