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Consider two differentiable functions \( f(x), g(x) \) satisfying
\( \mathrm{P} \) \( 6 \int f(x) g(x) d x=x^{6}+3 x^{4}+3 x^{2}+c \) and \( 2 \int \frac{g(x) d x}{f(x)}=x^{2}+c \),

W where \( f(x)0 \forall x \in R \).
\( \int(g(x)-f(x)) d x \) is equal to
(1) \( \frac{x^{4}}{4}-\frac{x^{2}}{2}+x+c \)
(2) \( \frac{x^{4}}{4}+\frac{x^{2}}{2}-\frac{x^{3}}{3}-x+c \)
(3) \( \frac{x^{4}}{4}-\frac{x^{3}}{3}+\frac{x^{2}}{2}-x+c \)
(4) \( \frac{x^{4}}{4}+\frac{x^{3}}{3}+c \)
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