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By the substitutions used to change equation to and by the reduction formula,, verify the following reduction formula (where [math]b^2-4ac \lt 0[/math]):

[[math]] \int \frac{dx}{(ax^2+bx+c)^n} = \frac{2ax+b}{(n-1)(4ac-b^2)(ax^2+bx+c)^{n-1}} [[/math]]

[[math]] + \frac{2a(2n-3)}{(n-1)(4ac-b^2)} \int \frac{dx}{(ax^2+bx+c)^{n-1}} . [[/math]]