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Find the following integrals:(i) int(x+...

Find the following integrals:(i) `int(x+2)/(2x^2+6x+5)dx` (ii) `int(x+3)/(sqrt(5-4x+x^2))dx`

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To solve the integrals given in the question, we will break down each part step by step. ### Part (i): Find the integral \(\int \frac{x+2}{2x^2 + 6x + 5} \, dx\) **Step 1: Simplify the integrand** We start by rewriting the integrand. We can express \(x + 2\) as a linear combination of the derivative of the denominator \(2x^2 + 6x + 5\). Let \(f(x) = 2x^2 + 6x + 5\). The derivative is: ...
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