TS EAMCET · Maths · Indefinite Integration
If \(\frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)
- A \(-\frac{1}{2}\)
- B \(\frac{1}{2}\)
- C \(1\)
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \quad \frac{x+1}{\left(x^2+1\right)(x-1)^2}=\frac{A x+B}{x^2+1}+\frac{C}{x-1}+\frac{D}{(x-1)^2} \\ & (x+1)=(A x+B)(x-1)^2+C(x-1)\left(x^2+1\right)+D\left(x^2+1\right) \\ & \begin{array}{r} \text { Put } x=1 \\ 2=2 D \Rightarrow D=1 \\ x+1=(A x+B)\left(x^2+1-2…
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