If \( \int \frac{(2 x+3) d x}{x(x+1)(x+2)(x+3)+1}=C-\frac{1}{f(x)} \) where \( f(x) \) is of the...

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If \( \int \frac{(2 x+3) d x}{x(x+1)(x+2)(x+3)+1}=C-\frac{1}{f(x)} \) where \( f(x) \) is of the form of \( a x^{2}+b x+c \), then \( (a+b+c) \) equals
(a) 4
(b) 5
(c) 6
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