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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int {\frac{{1 + x + \sqrt {x + {x^2}} }}{{\sqrt x \, + \sqrt {1 + x} }}\,\,dx = } $
  • A
    $1/2\sqrt {1 + x} + c$
  • ✓
    $2/3{(1 + x)^{3/2}} + c$
  • C
    $\sqrt {1 + x} + c$
  • D
    $2{(1 + x)^{3/2}} + c$
✓

Answer

Correct option: B.
$2/3{(1 + x)^{3/2}} + c$
b
(b) $\int {\frac{{1 + x + \sqrt {x + {x^2}} }}{{\sqrt x + \sqrt {1 + x} }}dx} $$ = \int {\frac{{\sqrt {1 + x} [\sqrt {1 + x} + \sqrt x ]}}{{(\sqrt x + \sqrt {1 + x} )}}\,dx} $
$ = \int {\sqrt {1 + x\,} } dx = \frac{2}{3}{(1 + x)^{3/2}} + c$.

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