Given $\frac{d}{dx}(\frac{1}{2x+1}) = -\frac{2}{(2x+1)^2}$, determine $\int \frac{6}{(2x+1)^2} dx$.
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To do this, we can use the binomial theorem. The binomial theorem states that for any positive integer n, the expansion of (a+b)^n can be written as the sum of the terms of the form C(n,k) * a^(n-k) * b^k, where C(n,k) is the binomial coefficient. In our case, a Show more…
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