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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {x\sqrt {2x + 3} } \;dx = $
  • ✓
    $\frac{x}{3}{(2x + 3)^{3/2}} - \frac{1}{{15}}{(2x + 3)^{5/2}} + c$
  • B
    $\frac{x}{3}{(2x + 3)^{3/2}} + \frac{1}{{15}}{(2x + 3)^{5/2}} + c$
  • C
    $\frac{x}{2}{(2x + 3)^{3/2}} + \frac{1}{6}{(2x + 3)^{5/2}} + c$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{x}{3}{(2x + 3)^{3/2}} - \frac{1}{{15}}{(2x + 3)^{5/2}} + c$
a
(a)$\int_{}^{} {x{{(2x + 3)}^{1/2}}dx} $
$ = x\frac{{{{(2x + 3)}^{3/2}}}}{{3/2}}\frac{1}{2} - \int_{}^{} {\frac{{{{(2x + 3)}^{3/2}}}}{{3/2}}\frac{1}{2}\,dx + c} $ $ = \frac{1}{3}x{(2x + 3)^{3/2}} - \frac{1}{3}\int_{}^{} {{{(2x + 3)}^{3/2}}dx + c} $
$ = \frac{1}{3}x{(2x + 3)^{3/2}} - \frac{1}{{15}}{(2x + 3)^{5/2}} + c.$

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