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Q28  Integrate the functions \frac{\cos x }{\sqrt { 1+ \sin x }}

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Given function  \frac{\cos x }{\sqrt { 1+ \sin x }},

Assume the 1+\sin x =t

 \therefore \cos x dx = dt

\implies \int \frac{\cos x }{\sqrt{1+\sin x}}dx = \int \frac{dt}{\sqrt t}

= \frac{t^{\frac{1}{2}}}{\frac{1}{2}} +C

= 2\sqrt t +C

Now, back substituted the value of t.

= 2{\sqrt{1+\sin x}} +C , where C is any constant value.

Posted by

Divya Prakash Singh

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