Evaluate x^ 8 (1-x^ 3 )^ 1 3 d x
Mathematics · JEE Main · NTA Exams — Integral Calculus
Evaluate \[\int \frac{x^{8}}{\left(1-x^{3}\right)^{\frac{1}{3}}} d x\]
- \(\frac{-\left(1-x^{3}\right)^{\frac{1}{3}}}{8}+\frac{2\left(1-x^{3}\right)^{\frac{5}{3}}}{5}-\frac{\left(1-x^{3}\right)^{\frac{2}{3}}}{2}+c\)
- \(\frac{\left(1-x^{3}\right)^{\frac{1}{3}}}{8}+\frac{2\left(1-x^{3}\right)^{\frac{5}{3}}}{5}+\frac{\left(1-x^{3}\right)^{\frac{2}{3}}}{2}+c\)
- \(\frac{\left(1-x^{3}\right)^{\frac{4}{3}}}{4}+\frac{2\left(1-x^{3}\right)^{\frac{5}{3}}}{5}+c\)
- None of these
Answer
(A) - (1-x^ 3 )^ 1 3 8 + 2 (1-x^ 3 )^ 5 3 5 - (1-x^ 3 )^ 2 3 2 +c
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