The solution for x of the equation $integral subscript square root of 2 end subscript superscript straight x fraction numerator dt over denominator straight t square root of straight t squared minus 1 end root end fraction space equals straight pi over 2 space is$

2

π

$square root of 3 divided by 2$
$2 square root of 2$

Solution

integral subscript square root of 2 end subscript superscript straight x space fraction numerator dt over denominator straight t square root of straight t squared minus 1 end root end fraction space equals space straight pi over 2 left square bracket sec to the power of negative 1 end exponent right square bracket subscript square root of 2 end subscript superscript straight x space equals space straight pi over 2 sec to the power of negative 1 end exponent space straight x space minus space straight pi over 4 space equals space straight pi over 2 sec to the power of negative 1 end exponent space straight x space space equals space fraction numerator 3 straight pi over denominator 4 end fraction straight x space equals space minus space square root of 2

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