Question

Evaluate: $\int \frac{dx}{\sqrt{x^2+1}}$

• A. $\text{arc}$ $\cos h\left(x\right)+c$
• B. $\sin h\left(x\right)+c$
• C. $\text{arc}\sin h\left(x\right)+c$
• D. None of these

Answer 1

Answer: (C)

$\text{arc}\sin h\left(x\right)+c$

Let $I=\int \frac{dx}{\sqrt{x^2+1}}$
We know that. $\int \frac{dx}{\sqrt{x^2+a^2}}={\sinh }^{-1}\frac{x}{a}$
$\therefore I={\sinh }^{-1}\frac{x}{1}+C$
$I=arc\sinh \left(x\right)+C$