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