If \( \int \frac{d x}{x^{4}\left(1+x^{3}\right)^{2}}=a \ln \left|\frac{1+x^{3}}{x^{3}}\right|+\f...
If \( \int \frac{d x}{x^{4}\left(1+x^{3}\right)^{2}}=a \ln \left|\frac{1+x^{3}}{x^{3}}\right|+\frac{b}{x^{3}}+\frac{c}{1+x^{3}}+d \), then (where \( d \) is arbitrary constant)
(a) \( a=\frac{1}{3}, b=\frac{1}{3}, x=\frac{1}{3} \)
(b) \( a=\frac{2}{3}, b=-\frac{1}{3}, c=\frac{1}{3} \)
(c) \( a=\frac{2}{3}, b=-\frac{1}{3}, c=-\frac{1}{3} \)
(d) \( a=\frac{2}{3}, b=\frac{1}{3}, c=-\frac{1}{3} \)
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