x^ 2 +1 [ [x^ 2 +1 ]-2 x ] x^ 4 d x is equal to
Mathematics · JEE Main · NTA Exams — Integral Calculus
\(\int \frac{\sqrt{x^{2}+1}\left[\log \left[x^{2}+1\right]-2 \log x\right]}{x^{4}} d x\) is equal to
- \(\frac{\left[x^{2}+1\right]^{3 / 2}}{x^{3}}\left[\frac{2}{3}-\log \left(\frac{x^{2}+1}{x^{2}}\right)\right]+c\)
- \(\frac{\left[x^{2}+1\right]^{3 / 2}}{3 x^{3}}\left[\log \left(\frac{x^{2}+1}{x^{2}}\right)\right]+c\)
- \(\frac{\left[x^{2}+1\right]^{3 / 2}}{3 x^{3}}\left[\frac{2}{3}-\log \left(\frac{x^{2}+1}{x^{2}}\right)\right]+c\)
- None of these
Answer
(C) [x^ 2 +1 ]^ 3 / 2 3 x^ 3 [ 2 3 - ( x^ 2 +1 x^ 2 ) ]+c
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