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Integrals of (px + q) over a quadratic

Quadratic forms

Concept 7 of 17 in Integrals

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Think about this

∫2x+2x2+2x+3 dx\int \frac{2x + 2}{x^2 + 2x + 3}\,dx =log⁡∣x2+2x+3∣+c= \log|x^2 + 2x + 3| + c, because the top is the derivative of the bottom. What if the top is 2x+72x + 7 instead?