If \( I=\int e^{x} \frac{x^{3}+3 x^{2}+4}{(x+1)^{3}} d x \), then \( I \) equals
(a) \( e^{x}\le...
If \( I=\int e^{x} \frac{x^{3}+3 x^{2}+4}{(x+1)^{3}} d x \), then \( I \) equals
(a) \( e^{x}\left(\frac{x^{2}-x+1}{(x+1)^{2}}\right)+C \)
(b) \( e^{x}\left(\frac{x^{2}-x+1}{(x+1)^{2}}\right)+C \)
(c) \( e^{x}\left(\frac{x^{2}+2 x-2}{(x+1)^{2}}\right)+C \)
(d) \( e^{x}\left(\frac{x^{2}+2 x-1}{(x+1)^{2}}\right)+C \)
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