Find , where…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Find

\displaystyle \int \frac{dx}{\sqrt{x^{2}+a^{2}}}

, where

a>0

. (a)

\dfrac{1}{a}\tan^{-1}\!\left(\dfrac{x}{a}\right)+C

(b)

\dfrac{x}{\sqrt{x^{2}+a^{2}}}+C

(c)

\ln|x+\sqrt{x^{2}+a^{2}}|+C

(d)

\sin^{-1}\!\left(\dfrac{x}{a}\right)+C