ExamBro
ExamBro
AP EAMCET · Maths · Indefinite Integration

\(\int \frac{5 \tan x}{(\tan x)-2} d x=\alpha x+\beta \log |\sin x-2 \cos x|\) \(+\gamma\), then \(\alpha-\beta=\)

  1. A –1
  2. B 2
  3. C 0
  4. D 1
Verified Solution

Answer & Solution

Correct Answer

(A) –1

Step-by-step Solution

Detailed explanation

\(\int \frac{5 \tan x}{\tan x-2} d x=\int \frac{5 \sin x}{\sin x-2 \cos x} d x\) Put, \(5 \sin x=\alpha(\sin x-2 \cos x)+\) \[ \begin{array}{r} \beta \frac{d}{d x}(\sin x-2 \cos x) \\ 5 \sin x=\alpha(\sin x-2 \cos x)+\beta(\cos x+2 \sin x) \end{array} \] On comparison of…