Question

$\log\lbrack 1 + \sqrt{1 - e^{2x}}\rbrack - x + c$

• A. $\int_{}^{}\frac{3x^{2}}{\sqrt{9 - 16x^{6}}}\mspace{6mu} dx =$
• B. $\frac{1}{4}\sin^{- 1}\left( \frac{4x^{3}}{3} \right) + c$
• C. $\frac{1}{3}\sin^{- 1}\left( \frac{4x^{3}}{3} \right) + c$
• D. $\frac{1}{4}\sin^{- 1}x^{3} + c$

Answer 1

Answer: (D)

$\frac{1}{4}\sin^{- 1}x^{3} + c$

Answer 2

Put $\frac{1}{2}{logtan}\left( \frac{x}{2} + \frac{\pi}{6} \right) + c$ then

${logcot}\left( \frac{x}{2} + \frac{\pi}{6} \right) + c$

$\frac{1}{2}{logcot}\left( \frac{x}{2} + \frac{\pi}{6} \right) + c$