TS EAMCET · Maths · Indefinite Integration
\(\int \frac{1}{(x-2)\left(x^2+1\right)} d x=\)
- A \(\log \frac{\sqrt{x^2+1}}{|x-2|}+2 \tan ^{-1} x+c\)
- B \(\log \frac{|x-2|}{x^2+1}+2 \tan ^{-1} x+c\)
- C \(\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{7+x^2}}+2 \tan ^{-1} x\right]+c\)
- D \(\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{1+x^2}}-2 \tan ^{-1} x\right]+c\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{5}\left[\log \frac{|x-2|}{\sqrt{1+x^2}}-2 \tan ^{-1} x\right]+c\)
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Detailed explanation
\(\int \frac{d x}{(x-2)\left(x^2+1\right)}\)…
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