Question

\(\displaystyle \int \frac{dx}{x^{2}+5}=\ \ ?\)

• A. \(\tan^{-1}\!\frac{x}{5}+k\)
• B. \(\tan^{-1}\!\frac{x}{\sqrt5}+k\)
• C. \(\dfrac{1}{\sqrt5}\tan^{-1}\!\frac{x}{\sqrt5}+k\)
• D. \(\sqrt5\,\tan^{-1}\!\frac{x}{\sqrt5}+k\)

Hint:

Memorize: $\int \frac{dx}{x^2+a^2}=\frac{1}{a}\arctan\!\frac{x}{a}$.

Answer 1

The Correct Option is C

Standard form: \[ \int\frac{dx}{x^{2}+a^{2}}=\frac{1}{a}\tan^{-1}\!\left(\frac{x}{a}\right)+C. \] Here \(a^{2}=5\Rightarrow a=\sqrt5\). Substitute to get the answer.