If I = (2 x +3) dx ( x ^ 2 +2 x +3 ) x ^ 2 +2 x +4 , then I equals
Mathematics · JEE Advanced · NTA Exams — Integral Calculus
If \(\mathrm{I}=\int \frac{(2 \mathrm{x}+3) \mathrm{dx}}{\left(\mathrm{x}^{2}+2 \mathrm{x}+3\right) \sqrt{\mathrm{x}^{2}+2 \mathrm{x}+4}},\)then I equals
- \[\log \left|\frac{\sqrt{x^{2}+2 x+4}-1}{\sqrt{x^{2}+2 x+4}+1}\right|+c\]
- \[\log \left|\frac{\sqrt{x^{2}+2 x+4}-1}{\sqrt{x^{2}+2 x+4}+1}\right|+\tan ^{-1}\left(\frac{x+2}{3}\right)+c\]
- \(\log \tan ^{-1}\left(\frac{\sqrt{\mathrm{x}+3}}{2}\right)+\mathrm{c}\)
- None
Answer
(D) None
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