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AP EAMCET · Maths · Definite Integration

If \(729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x=a+\log b\), then \(a-b=\)

  1. A 4
  2. B \(-\frac{4}{5}\)
  3. C \(\frac{4}{5}\)
  4. D -4
Verified Solution

Answer & Solution

Correct Answer

(A) 4

Step-by-step Solution

Detailed explanation

\(\mathrm{I}=729 \int_1^3 \frac{1}{x^3\left(x^2+9\right)^2} d x\) Let \(\frac{1}{x^3\left(x^2+9\right)^2}=\frac{\mathrm{A}}{x}+\frac{\mathrm{B}}{x^2}+\frac{C}{x^3}+\frac{\mathrm{D} x+\mathrm{E}}{x^2+9}+\frac{\mathrm{F} x+\mathrm{G}}{\left(x^2+9\right)^2}\)…