Aspire Faculty ID #15123 · Topic: JAMIA MILLIA ISLAMIA MCA 2018 · Just now
JAMIA MILLIA ISLAMIA MCA 2018

Find the value of $\displaystyle \int \dfrac{x,dx}{\sqrt{x^2 + 4}}$

Solution

Let $x = 2\tan\theta$, $dx = 2\sec^2\theta,d\theta$ $\Rightarrow I = \int \dfrac{2\tan\theta \cdot 2\sec^2\theta}{2\sec\theta}d\theta = 2\int \tan\theta\sec\theta,d\theta = 2\sec\theta + C = \dfrac{1}{2}\sqrt{x^2+4}+C$ Hence equivalent to $\dfrac{1}{4}\sec^{-1}\left(\dfrac{x}{2}\right)$
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