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Integrate the rational functions(2x)/((...

Integrate the rational functions`(2x)/((x^2+1)(x^2+3)`

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To integrate the rational function \( \frac{2x}{(x^2+1)(x^2+3)} \), we can follow these steps: ### Step 1: Substitution Let \( t = x^2 \). Then, differentiating both sides gives: \[ dt = 2x \, dx \quad \Rightarrow \quad dx = \frac{dt}{2x} \] This substitution will help us simplify the integral. ...
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