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Indefinite Integration — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsIndefinite Integration1 Mark
MCQ
$\int \frac{\cos 2 x-1}{\cos 2 x+1} \cdot d x=$
  • A
    tan x – x + c
  • B
    x + tan x + c
  • ✓
    x – tan x + c
  • D
    -x – cot x + c
✓

Answer

Correct option: C.
x – tan x + c
$x – tan x + c$
Hint :
$\int \frac{\cos 2 x-1}{\cos 2 x+1} d x$
$=\int \frac{-(1-\cos 2 x)}{1+\cos 2 x} d x$
$=\int \frac{-2 \sin ^2 x}{2 \cos ^2 x} d x$
$=-\int\left(\sec ^2 x-1\right) d x $
$ =-\tan x+x+c$

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