integrate: 2x^2 / x^2 + 4 dx how do know which substitution to use here and what happens to the numerator???
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Originally Posted by razorfever integrate: 2x^2 / x^2 + 4 dx how do know which substitution to use here and what happens to the numerator??? First do some long division to turn the integrand into $\displaystyle 2 - \frac{8}{x^2 + 4}$. Then you work with the fact that $\displaystyle \int{\frac{1}{a^2 + x^2}\,dx} = \frac{1}{a}\arctan{\left ( \frac{x}{a} \right )} + C$.
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