Question

\[\int\frac{\sec^2 x}{\sqrt{4 + \tan^2 x}} dx\]

Answer 1

 

` ∫   { sec^2 x  dx}/{\sqrt{4 + tan^2 x}} `

\`text{ let } tan  x }= t `
\[ \Rightarrow \sec^2 x dx = dt\]
Now, ` ∫   { sec^2 x  dx}/{\sqrt{4 + tan^2 x}} `
\[ = \int\frac{dt}{\sqrt{2^2 + t^2}}\]
\[ = \text{ log } \left| t + \sqrt{4 + t^2} \right| + C\]
\[ = \text{ log }\left| \text{ tan x }+ \sqrt{4 + \tan^2 x} \right| + C\]