JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{d x}{\left(x^{2}+x+1\right)^{2}}=a \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)+b\left(\frac{2 x+1}{x^{2}+x+1}\right)+C\) \(x>0\) where \(C\) is the constant of integration, then the value of \(9(\sqrt{3} \mathrm{a}+\mathrm{b})\) is equal to ... .
- A \(13\)
- B \(15\)
- C \(17\)
- D \(8\)
Answer & Solution
Correct Answer
(B) \(15\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{d x}{\left[\left(x+\frac{1}{2}\right)^{2}+\frac{3}{4}\right]^{2}}\) \(\int \frac{d t}{\left(t^{2}+\frac{3}{4}\right)^{2}}\left(\text { Put } x+\frac{1}{2}=t\right)\)…
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