AP EAMCET · Maths · Indefinite Integration
\(\int \frac{x^4-16 x^2+2 x+8}{x^3-4 x^2+2} d x=\)
- A \(\frac{x^2+8 x+c}{2}\)
- B \(x^2+8 x+c\)
- C \(x^3-4 x+c\)
- D \(\frac{x^2-8 x+c}{2}\)
Answer & Solution
Correct Answer
(A) \(\frac{x^2+8 x+c}{2}\)
Step-by-step Solution
Detailed explanation
\(\frac{x^4-16 x^2+2 x+8}{x^3-4 x^2+2} = x+4\) \(\int (x+4) dx\) \(=\frac{x^2}{2} + 4x + c\) \(=\frac{x^2+8 x+c}{2}\)
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