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Question
\[\int\frac{\cos x}{\sqrt{4 + \sin^2 x}} dx\]
Sum
Solution
` ∫ { 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}} `
\[ = \int\frac{dt}{\sqrt{2^2 + t^2}}\]
\[ = \text{ log } \left| t + \sqrt{4 + t^2} \right| + C\]
\[ = \text{ log } \left| \sin x + \sqrt{4 + \sin^2 x} \right| + C\]
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