\[ \int_{a}^{b} x^{n-1} \frac{\left((n-2) x^{2}+(n-1)(a+b) x+n a b\right)}{(x+a)^{2}(x+b)^{2}} d...

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\[
\int_{a}^{b} x^{n-1} \frac{\left((n-2) x^{2}+(n-1)(a+b) x+n a b\right)}{(x+a)^{2}(x+b)^{2}} d x
\]
(a) \( \frac{b^{n-1}-a^{n-1}}{2(a-b)} \)
(b) \( \frac{b^{n-1}-a^{n-1}}{2(a+b)} \)
(c) \( \frac{b^{n-1}+a^{n-1}}{2(a+b)} \)
(d) \( \frac{b^{n-1}+a^{n-1}}{(a+b)} \)
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