Find the integral of (2(3x+2))/(3x^2+4x+9).
Start by expanding out the bracket on the top of the fraction to get (6x+4)/(3x2+4x+9). Then using the trick of identifying that the fraction is in the form [g(x)]/[f(x)] where f’(x)=g(x), the solution is ln(f(x)). Hence in this case would be ln(3x2+4x+9). To confirm a student understands why this is the case I would then get them to differentiate ln(3x2+4x+9) to see how this method works.
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