AP EAMCET · Maths · Indefinite Integration
If \(\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}\) then \(B D-A C=\)
- A \(\frac{3}{8}\)
- B \(\frac{1}{8}\)
- C \(1\)
- D \(0\)
Answer & Solution
Correct Answer
(A) \(\frac{3}{8}\)
Step-by-step Solution
Detailed explanation
Since, given \(\begin{aligned} & \frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1} \\ & \Rightarrow(A x+B)\left(x^2-\sqrt{2} x+1\right)+(C x+D)\left(x^2+\sqrt{2} x+1\right)=1 \end{aligned}\) If \(x=0 \Rightarrow B+D=1\) Equating co-efficient of…
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