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Integrals — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsIntegrals1 Mark
MCQ
Evaluate: $\int \frac{\sec ^2 x}{2+\tan x} d x$
  • A
    $\log |\tan x|+C$
  • B
    $\log |2-\tan x|+C$
  • ✓
    $\log |2+\tan x|+C$
  • D
    none of these
✓

Answer

Correct option: C.
$\log |2+\tan x|+C$
(c) : Let $I=\int \frac{\sec ^2 x}{2+\tan x} d x$
Put $2+\tan x=t \Rightarrow \sec ^2 x d x=d t$
$
\therefore \quad I=\int \frac{d t}{t}=\log |t|+C=\log |2+\tan x|+C
$

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