If the integrand is a rational function of \( x \) and fractional p...

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If the integrand is a rational function of \( x \) and fractional powers of a linear fractional function of the form \( \frac{a x+b}{c x+d} \), then rationalization of the integral is affected by the substitution \( \frac{a x+b}{c x+d}=t^{m} \), where \( m \) is 1.c.m. of fractional powers of \( \frac{a x+b}{c x+d} \)
\[
\begin{array}{l}
\text { If } I=\int \frac{d x}{\sqrt[3]{(x+1)^{2}(x-1)^{4}}} \\
-K \sqrt[3]{\frac{1+x}{1-x}}+C
\end{array}
\]
then \( K \) is equal to
(a) \( 2 / 3 \)
(b) \( -3 / 2 \)
(c) \( 1 / 3 \)
(d) \( 1 / 2 \)
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