AP EAMCET · Maths · Indefinite Integration
\(\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x=\)
- A \(\frac{x^7}{5 x^7+x+2}+c\)
- B \(\frac{x^7}{2\left(5 x^7+x+2\right)}+c\)
- C \(\frac{1}{2\left(5 x^7+x+2\right)}+c\)
- D \(\frac{-x^7}{2\left(5 x^7+x+2\right)}+c\)
Answer & Solution
Correct Answer
(B) \(\frac{x^7}{2\left(5 x^7+x+2\right)}+c\)
Step-by-step Solution
Detailed explanation
\(I=\int \frac{3 x^9+7 x^8}{\left(x^2+2 x+5 x^8\right)^2} d x\) \(I=\int \frac{3 x^9+7 x^8}{x^{16}\left(\frac{1}{x^6}+\frac{2}{x^7}+5\right)^2} d x \Rightarrow I=\int \frac{3 x^{-7}+7 x^{-8}}{\left(\frac{1}{x^6}+\frac{2}{x^7}+5\right)^2} d x\) Let…
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