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Integrate the functions(5x+3)/(sqrt(x^2+...

Integrate the functions`(5x+3)/(sqrt(x^2+4x+10))`

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To solve the integral \(\int \frac{5x + 3}{\sqrt{x^2 + 4x + 10}} \, dx\), we will follow these steps: ### Step 1: Rewrite the numerator We can express the numerator \(5x + 3\) in terms of the derivative of the denominator \(x^2 + 4x + 10\). We note that the derivative of \(x^2 + 4x + 10\) is \(2x + 4\). Let’s express \(5x + 3\) as: \[ 5x + 3 = a(2x + 4) + b ...
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