Question

Solve: $\int \frac{1}{\sqrt{21+4x-x^2}}dx$

Answer 1

Now,

$\int \frac{1}{\sqrt{21+4x-x^2}}dx$

$=\int \frac{1}{\sqrt{25-(4-4x+x^2)}}dx$

$=\int \frac{1}{\sqrt{5^2-(x-2{)}^2}}dx$

$={\sin }^{-1}\frac{x-2}{5}+c$ [ Where $c$ is integrating constant.