Evaluate the following definite integral: `int_0^2 1/(4+x-x^2)dx`

Explanation

`=int_{0}^{2} frac{1}{4+x-x^{2}} d x`


Since it is a quadratic equation we are trying to make it a complete square
`

=int_{0}^{2} frac{1}{-(-4-x+x^{2})} d x `
`
=int_{0}^{2} frac{1}{-(-4-x+x^{2}+frac{1}{4}-frac{1}{4})} d x `
`
=int_{0}^{2} frac{1}{-((x-frac{1}{2})^{2}-frac{17}{4})} d x `
`
=int_{0}^{2} frac{1}{(frac{sqrt{17}}{2})^{2}-((x-frac{1}{2})^{2})} d x`

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