Question:
\(\displaystyle \int \frac{dx}{1+36x^{2}}=\) ?
\(\displaystyle \int \frac{dx}{1+36x^{2}}=\) ?
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Standard form: $\displaystyle \int\frac{dx}{a^{2}+x^{2}}=\frac{1}{a}\tan^{-1}\!\frac{x}{a}+C$.
Updated On: Oct 17, 2025
- \(6\tan^{-1}(6x)+k\)
- \(3\tan^{-1}(6x)+k\)
- \(\dfrac{1}{6}\tan^{-1}(6x)+k\)
- \(\tan^{-1}(6x)+k\)
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The Correct Option is C
Solution and Explanation
Let \(u=6x\Rightarrow du=6\,dx\Rightarrow dx=\dfrac{du}{6}\). Then
\[
\int \frac{dx}{1+(6x)^{2}}=\frac{1}{6}\int \frac{du}{1+u^{2}}
=\frac{1}{6}\tan^{-1}u+k=\frac{1}{6}\tan^{-1}(6x)+k.
\]
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