AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x}{x^3-3 x+2} d x=\)
- A \(\frac{2}{9} \log \left|\frac{x-1}{x+2}\right|+c\)
- B \(\frac{2}{9} \log \left|\frac{x+2}{x-1}\right|+c\)
- C \(\frac{1}{3} \frac{1}{x-1}+\frac{2}{9} \log \left|\frac{x-1}{x+2}\right|+c\)
- D \(-\frac{1}{3} \frac{1}{(x-1)}+\frac{2}{9} \log \left|\frac{x-1}{x+2}\right|+c\)
Answer & Solution
Correct Answer
(D) \(-\frac{1}{3} \frac{1}{(x-1)}+\frac{2}{9} \log \left|\frac{x-1}{x+2}\right|+c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x}{x^3-3 x+2} d x=\int \frac{x}{(x-1)^2} \frac{d x}{(x+2)}\) Now, by partial fraction method \[ \begin{aligned} & \frac{x}{(x-1)^2(x+2)}=\frac{A}{(x-1)}+\frac{B}{(x-1)^2}+\frac{C}{(x+2)} \\ & \Rightarrow x=A(x-1)(x+2)+B(x+2)+C(x-1)^2 \end{aligned} \] On comparing…
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