Prove that begin mathsize 20px style integral fraction numerator d x over denominator square root of open parentheses 1 plus sin x close parentheses end root end fraction equals square root of 2 log open vertical bar tan open parentheses 1 over 8 straight pi plus 1 fourth straight x close parentheses close vertical bar plus c end style

Asked by sunil2791 | 26th May, 2017, 01:01: PM

Expert Answer:

begin mathsize 16px style straight I equals integral fraction numerator dx over denominator square root of 1 plus sinx end root end fraction
straight I equals integral fraction numerator dx over denominator square root of 1 plus cos open parentheses begin display style straight pi over 2 end style minus straight x close parentheses end root end fraction
straight I equals integral fraction numerator dx over denominator square root of 2 cos squared open parentheses begin display style straight pi over 4 end style minus begin display style straight x over 2 end style close parentheses end root end fraction
We space will space appreciate space if space you space solve space it space further space and space post space it space to space us. end style

Answered by Sneha shidid | 26th May, 2017, 04:45: PM