First slide

Methods of integration

Question

$\int (x + 1)^{3 / 2} [\sin^{- 1} (\log x) + \cos^{- 1} (\log x)] dx$ is equal to

Moderate

A

$\frac{2 π}{5} (x + 1)^{5 / 2} + C$
B

$\frac{π}{5} (x + 1)^{5 / 2} + C$
C

$does not exist$
D

None of these

Solution

$∵ \sin^{- 1} x and \cos^{- 1} x are defined for [- 1, 1]$
$For x > e, \log x > 1$
$\Rightarrow \sin^{- 1} (\log x) + \cos^{- 1} (\log x) is not defined .$

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