TS EAMCET · Maths · Indefinite Integration
\(\int x \operatorname{Tan}^{-1} \sqrt{\frac{1+x^2}{1-x^2}} d x=\)
- A \(\frac{x^2}{4}\left(\pi-\operatorname{Cos}^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^2}+\mathrm{c}\)
- B \(\frac{x^2}{4}\left(\pi-\operatorname{Cos}^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^4}+c\)
- C \(\frac{x^2}{4}\left(\pi+\operatorname{Cos}^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^4}+\mathrm{c}\)
- D \(\frac{x^2}{4}\left(\pi+\operatorname{Cos}^{-1} x^2\right)-\frac{1}{4} \sqrt{1-x^2}+\mathrm{c}\)
Answer & Solution
Correct Answer
(B) \(\frac{x^2}{4}\left(\pi-\operatorname{Cos}^{-1} x^2\right)+\frac{1}{4} \sqrt{1-x^4}+c\)
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