MHT CET · Maths · Indefinite Integration
\(\int \frac{x}{\sqrt{1-2 x^4}} \mathrm{~d} x=\) (Where \(C\) is a constant of integration)
- A \(\frac{1}{2 \sqrt{2}} \sin ^{-1}\left(\sqrt{2} x^2\right)+C\)
- B \(\frac{1}{2 \sqrt{2}} \sin ^{-1}\left(2 \sqrt{2} x^2\right)+C\)
- C \(\frac{1}{2} \sin ^{-1}(2 x)+C\)
- D \(\frac{1}{\sqrt{2}} \sin ^{-1}(\sqrt{2} x)+C\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{2 \sqrt{2}} \sin ^{-1}\left(\sqrt{2} x^2\right)+C\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x}{\sqrt{1-2 x^4}} \mathrm{~d} x=\frac{1}{2 \sqrt{2}} \int \frac{2 \sqrt{2} x \mathrm{~d} x}{\sqrt{1-\left(\sqrt{2} x^2\right)^2}}=\frac{1}{2 \sqrt{2}} \sin ^{-1}\left(\sqrt{2} x^2\right)\)
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