The value of $integral subscript 0 superscript pi divided by 2 end superscript fraction numerator left parenthesis sin space x space plus space cos space x right parenthesis squared over denominator square root of 1 plus space sin space 2 x end root end fraction space d x space i s$

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Solution

integral subscript 0 superscript straight pi divided by 2 end superscript fraction numerator left parenthesis sin space straight x space plus cos space straight x right parenthesis squared over denominator square root of left parenthesis sin space straight x space plus space cos space straight x right parenthesis squared end root end fraction space dx space equals space integral subscript 0 superscript straight pi divided by 2 end superscript space left parenthesis sin space straight x space plus space cos space straight x right parenthesis space dx space equals space vertical line minus space cos space straight x space plus space sin space straight x vertical line subscript 0 superscript straight pi divided by 2 end superscript space equals space 2

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