AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^8+4}{x^4-2 x^2+2} d x=A x^5+B x^3+C x+k\), then \(5 A+3 B+C=\)
- A \(7\)
- B \(5\)
- C \(3\)
- D \(1\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \int \frac{x^8+4}{x^4-2 x^2+2} d x=\int \frac{x^8+4 x^4+4-4 x^4}{x^4-2 x^2+2} d x \\ & =\int \frac{\left(x^4+2\right)^2-\left(2 x^2\right)^2}{x^4-2 x^2+2} d x=\int x^4+2+2 x^2 d x \\ & =\frac{x^5}{5}+\frac{2 x^3}{3}+2 x+k \\ \Rightarrow & A=\frac{1}{5},…
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