TS EAMCET · Maths · Indefinite Integration
\(\int \frac{x^3+2 x}{x^4+4} d x=\)
- A \(\frac{1}{2}\left[\tan ^1\left(\frac{x^2}{2}\right)+\log \left(\frac{\sqrt{x^4+4}}{2}\right)\right]+C\)
- B \(\frac{1}{2} \tan ^1\left(\frac{x^2+2}{2 x}\right)+C\)
- C \(\frac{1}{2}\left[\tan ^1\left(\frac{x^2}{2}\right)-\log \left(\frac{\sqrt{x^4+4}}{4}\right)\right]+C\)
- D \(\frac{1}{\sqrt{2}} \tan ^1\left(\frac{x^2+1}{\sqrt{2} x}\right)+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2}\left[\tan ^1\left(\frac{x^2}{2}\right)+\log \left(\frac{\sqrt{x^4+4}}{2}\right)\right]+C\)
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