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AP EAMCET · Maths · Indefinite Integration

If \(x \neq \frac{-3}{\sqrt{2}}\), then \(\int \frac{x^2}{2 x^2+6 \sqrt{2} x+9} d x=\)

  1. A \(\frac{1}{2 \sqrt{2}}\left[(\sqrt{2} x+3)-6 \log |\sqrt{2} x+3|-\frac{9}{\sqrt{2} x+3}\right]+c\)
  2. B \(\frac{1}{2 \sqrt{2}}\left[\sqrt{2} x+3-6 \log |(\sqrt{2} x+3)|+\frac{9}{\sqrt{2} x+3}\right]+c\)
  3. C \(\sqrt{2} x+3-6 \log (\sqrt{2} x+3)+c\)
  4. D \(\log \left(2 x^2+6 \sqrt{2} x+9\right)+c\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{1}{2 \sqrt{2}}\left[(\sqrt{2} x+3)-6 \log |\sqrt{2} x+3|-\frac{9}{\sqrt{2} x+3}\right]+c\)

Step-by-step Solution

Detailed explanation

Given,…