Q. $\int_{}^{}{(x + 1)^{3/2}\lbrack\sin^{- 1}{(\log{x) + \cos^{- 1}{(\log{x)\rbrack dx}}}}}$ is equal to
A) $\frac{2\pi}{2}(x + 1)^{5/2} + c$
B) $\frac{\pi}{5}(x + 1)^{5/2} + c$
C) Does not exist
D) None of these
Explanation
(c)
$\because\sin^{- 1}x$ and $\cos^{- 1}x$ are defined for $\lbrack - 1,\ 1\rbrack$.
For $x > e,\log{x > 1}$
$\Rightarrow \sin^{- 1}{(\log{x) + \cos^{- 1}{(\log{x)}}}}$ is not defined.
Hence, the given integral does not exist.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.