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Integrate the functions(5x-2)/(1+2x+3x^2...

Integrate the functions`(5x-2)/(1+2x+3x^2)`

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To solve the integral of the function \(\frac{5x - 2}{1 + 2x + 3x^2}\), we will follow these steps: ### Step 1: Set Up the Integral Let \( I = \int \frac{5x - 2}{1 + 2x + 3x^2} \, dx \). ### Step 2: Express the Numerator in Terms of the Derivative of the Denominator We want to express \(5x - 2\) in a form that relates to the derivative of the denominator \(1 + 2x + 3x^2\). The derivative of the denominator is: \[ ...
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