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Evaluate: (i) int1/(x^2+6x+13)\ dx...

Evaluate: (i) `int1/(x^2+6x+13)\ dx`

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`int frac{d x}{x^{2}+6 x+13} d x `
`=int frac{d x}{x^{2}+2 times x times 3+9-9+13} `
`=int frac{d x}{(x+3)^{2}+2^{2}} `
`=frac{1}{2} tan ^{-1}(frac{x+3}{2})+C`
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