# How do you find the definite integral of #2 / (4+x^2) dx# from #[0, 2]#?

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To find the definite integral of ( \frac{2}{4+x^2} ) from 0 to 2, you can use the formula for integrating rational functions. First, perform a substitution: ( x = 2 \tan(\theta) ). This transforms the integral into a trigonometric form. Then, integrate with respect to ( \theta ) from ( \theta = 0 ) to ( \theta = \arctan(1) ). After integrating, convert back to the original variable ( x ). The result is approximately 0.7854.

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