_ ^ dx x + x - 2 = - Vidyadip

MCQ

$\int_{}^{} {\frac{{dx}}{{\sqrt x + \sqrt {x - 2} }} = } $

✓
$\frac{1}{3}[{x^{3/2}} - {(x - 2)^{3/2}}] + c$
B
$\frac{2}{3}[{x^{3/2}} - {(x - 2)^{3/2}}] + c$
C
$\frac{1}{3}[{(x - 2)^{3/2}} - {x^{3/2}}] + c$
D
$\frac{2}{3}[{(x - 2)^{3/2}} - {x^{3/2}}] + c$

✓

Answer

Correct option: A.

$\frac{1}{3}[{x^{3/2}} - {(x - 2)^{3/2}}] + c$

a
(a)$\int_{}^{} {\frac{{dx}}{{\sqrt x + \sqrt {x - 2} }} = \frac{1}{2}\int_{}^{} {\frac{{x - (x - 2)}}{{\sqrt x + \sqrt {x - 2} }}\,dx} } $
$ = \frac{1}{2}\int_{}^{} {(\sqrt x - \sqrt {x - 2} )\,dx} = \frac{1}{2}\left[ {\frac{{{x^{32}}}}{{32}} - \frac{{{{(x - 2)}^{32}}}}{{32}}} \right] + c$
$ = \frac{1}{3}\left\{ {{x^{32}} - {{(x - 2)}^{32}}} \right\} + c.$

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