TS EAMCET · Maths · Indefinite Integration
\(\int \frac{2 x+2}{\sqrt{x^2-4 x-5}} d x\) is equal to
- A \(\sqrt{x^2-4 x-5}+\log \left|x+\sqrt{x^2-4 x-5}\right|+C\)
- B \(\log \left|\sqrt{x^2-4 x-5}\right|-\sqrt{x^2-4 x-5}+C\)
- C \(\sqrt{x^2-4 x-5}+6 \log \left|(x-2)+\sqrt{x^2-4 x-5}\right|+C\)
- D \(2 \sqrt{x^2-4 x-5}+6 \log \left|(x-2)+\sqrt{x^2-4 x-5}\right|+C\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{x^2-4 x-5}+6 \log \left|(x-2)+\sqrt{x^2-4 x-5}\right|+C\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Let } I=\int \frac{2 x+2}{\sqrt{x^2-4 x-5}} d x \\ & 2 x+2=A \frac{d}{d x}\left(x^2-4 x-5\right)+B \\ & \Rightarrow \quad 2 x+2=A(2 x-4)+B \\ & \Rightarrow \quad 2 x+2=2 A x-4 A+B \\ & \end{aligned} \] Compare the coefficients of both sides, we get…
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