Question
Download Solution PDFEvaluate \(\rm \int \frac{dx}{x^{2}+4}\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- \(\rm \int \frac{dx}{x^{2}+a^{2}}=\frac{1}{a}tan^{-1}\frac{x}{a}+C\)
Calculation:
Given: \(\rm \int \frac{dx}{x^{2}+4}\)
Using the formula, \(\rm \int \frac{dx}{x^{2}+a^{2}}=\frac{1}{a}tan^{-1}\frac{x}{a}+C\)
\(\rm \Rightarrow\int \frac{dx}{x^{2}+4}=\int \frac{dx}{x^{2}+2^{2}}= \frac{1}{2}tan^{-1}\frac{x}{2}+C\)
Hence, the correct answer is option 2.
Last updated on Jun 20, 2025
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