TS EAMCET · Maths · Indefinite Integration
\[ \int \frac{1}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} d x= \]
- A \(\frac{1}{2} \sec ^{-1}\left(\mathrm{x}^2+2\right)+\mathrm{c}\)
- B \(-\operatorname{cosec~} \mathrm{h}^{-1}\left(\mathrm{x}^2+2\right)+\mathrm{c}\)
- C \(\frac{1}{2} \tan ^{-1}\left(x+\frac{2}{x}\right)+c\)
- D \(-\frac{1}{2} \cot ^{-1}\left(x+\frac{2}{x}\right)+c\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2} \sec ^{-1}\left(\mathrm{x}^2+2\right)+\mathrm{c}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {} \int \frac{d x}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} \\ & =\int \frac{x d x}{\left(x^2+2\right) \sqrt{\left(x^2+2\right)^2-1}}\end{aligned}\)…
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