Question

\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]

Answer 1

 

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