Question

$\int \frac{d x}{x^{\frac{5}{6}}\left(1+5 x^{\frac{1}{3}}\right) \sqrt{1+4 x^{\frac{1}{3}}}}$ equals
(where ' $c$ ' is a constant of integration)

• A. $6 \tan ^{-1}\left(\sqrt{\frac{1+4 x^{\frac{1}{3}}}{x^{\frac{1}{3}}}}\right)+c$
• B. $3 \ln \left|\frac{1+\sqrt{4+x^{-\frac{1}{3}}}}{1-\sqrt{4+x^{-\frac{1}{3}}}}\right|+c$
• C. $6 \cot ^{-1}\left(\sqrt{\frac{1+4 x^{\frac{1}{3}}}{x^{\frac{1}{3}}}}\right)+c$
• D. $3 \ln \left|\frac{1-\sqrt{4+x^{-\frac{1}{3}}}}{1+\sqrt{4+x^{-\frac{1}{3}}}}\right|+c$

Answer 1

Answer: (C)

Correct answer is (c) $6 \cot ^{-1}\left(\sqrt{\frac{1+4 x^{\frac{1}{3}}}{x^{\frac{1}{3}}}}\right)+c$