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int (sinx+cosx)/sqrt(1+sin2x)dx....

`int (sinx+cosx)/sqrt(1+sin2x)dx`.

Text Solution

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Let `I = int(sinx+cosx)/(sqrt(1+sin2x))dx=int(sinx+cosx)/(sqrt(sin^(2)x+cos^(2)x+2sinxcosx))dx`
` =int(sinx+cos)/(sqrt(sinx+cosx)^(2))dx = int1dx = x + C`
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