Question

Integrate the following function: $\int \frac{dx}{\sqrt{(1-{4x}^2)}}$

• A. $\frac{1}{2}{\sin }^{-1}2x+c$
• B. $-\frac{1}{2}{\sin }^{-1}2x+c$
• C. $\frac{1}{2}{\cos }^{-1}2x+c$
• D. $-\frac{1}{2}{\cos }^{-1}2x+c$

Answer 1

The correct option is A

$\frac{1}{2}{\sin }^{-1}2x+c$

$\int \frac{dx}{\sqrt{1-4x^2}}$

$=\frac{1}{2}\int \frac{dx}{\sqrt{(\frac{1}{2}{)}^2-x^2}}$

$=\frac{1}{2}\int \frac{dx}{\sqrt{(\frac{1}{2}{)}^2-x^2}}$

$=\frac{1}{2}{\sin }^{-1}\frac{x}{\frac{1}{2}}+c$

$=\frac{1}{2}{\sin }^{-1}2x+c$