If the integrand is a rational function of x and fractional powers of a linear fractional…
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
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 \(\frac{\mathrm{ax}+\mathrm{b}}{\mathrm{cx}+\mathrm{d}}=\mathrm{t}^{\mathrm{m}},\)where m is the L.C.M. of fractional powers of \(\frac{a x+b}{c x+d}\).
If \(I=\int \frac{d x}{\sqrt[4]{(x-1)^{3}(x+2)^{5}}}=A \sqrt[4]{\frac{x-1}{x+2}}+c\)then A is equal to
- \(\frac{1}{3}\)
- \(\frac{2}{3}\)
- \(\frac{3}{4}\)
- \(\frac{4}{3}\)
Answer
(D) 4 3
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