TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{\left(x^2-1\right)}{(x+1)^2 \sqrt{x\left(x^2+x+1\right)}} d x\) \(=A \tan ^{-1}\left(\sqrt{\frac{x^2+x+1}{x}}\right)+C\), in which \(C\) is a constant, then \(A\) equals to
- A \(\frac{1}{2}\)
- B \(3\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { Let } I=\int \frac{x^2-1}{(x+1)^2 \sqrt{x\left(x^2+x+1\right)}} d x \\ & \text { Now, } \frac{d}{d x}\left(\tan ^{-1} \sqrt{\frac{x^2+x+1}{x}}\right) \\ & =\frac{1}{1+\frac{x^2+x+1}{x}} \times \frac{d}{d x}\left(\sqrt{\frac{x^2+x+1}{x}}\right) \\ &…
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