JEE Mains · Maths · STD 12 - 7.2 definite integral
The integral \(16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) is equal to
- A \(\frac{11}{6}+\log _e 4\)
- B \(\frac{11}{12}+\log _e 4\)
- C \(\frac{11}{12}-\log _{ e } 4\)
- D \(\frac{11}{6}-\log _e 4\)
Answer & Solution
Correct Answer
(D) \(\frac{11}{6}-\log _e 4\)
Step-by-step Solution
Detailed explanation
\(I=16 \int \limits_1^2 \frac{d x}{x^3\left(x^2+2\right)^2}\) \(=16 \int \limits_1^2 \frac{d x}{x^3 x^4\left(1+\frac{2}{x^2}\right)^2}\) Let, \(1+\frac{2}{x^2}=t \Rightarrow \frac{-4}{x^3} d x=d t\)…
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