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7.1 inderfinite integral — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths7.1 inderfinite integral1 Mark
MCQ
$\int_{}^{} {{{(\sec x + \tan x)}^2}dx = } $
  • ✓
    $2(\sec x + \tan x) - x + c$
  • B
    $1/3{(\sec x + \tan x)^3} + c$
  • C
    $\sec x(\sec x + \tan x) + c$
  • D
    $2(\sec x + \tan x) + c$
✓

Answer

Correct option: A.
$2(\sec x + \tan x) - x + c$
a
(a)$\int_{}^{} {{{(\sec x + \tan x)}^2}dx} $
$ = \int_{}^{} {({{\sec }^2}x + {{\tan }^2}x + 2\sec x\tan x)\,dx} $
$ = \int_{}^{} {(2{{\sec }^2}x - 1 + 2\sec x\tan x)\,dx} $
$ = 2\tan x + 2\sec x - x + c = 2(\sec x + \tan x) - x + c.$

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