how is the integral of sec x = log tan (x/2+pi/4)?

Asked by Saisri Akondi | 26th Apr, 2014, 12:21: AM

Expert Answer:

I equals integral s e c x space d x  l e t space t equals s e c x rightwards double arrow d t equals tan squared x space d x  I equals integral fraction numerator t over denominator tan squared x end fraction d t equals integral fraction numerator t over denominator t squared minus 1 end fraction d t   equals integral open square brackets fraction numerator 1 over denominator 2 open parentheses t minus 1 close parentheses end fraction minus fraction numerator 1 over denominator 2 open parentheses t plus 1 close parentheses end fraction close square brackets d t  equals 1 half open square brackets ln open parentheses t minus 1 close parentheses minus ln open parentheses t plus 1 close parentheses close square brackets plus c  equals 1 half ln open square brackets fraction numerator t minus 1 over denominator t plus 1 end fraction close square brackets plus c  equals 1 half l straight n open square brackets fraction numerator s e c minus 1 over denominator s e c plus 1 end fraction close square brackets plus c  w h i c h space c a n space b e space e a s i l y space c o n v e r t e d space i n t o equals ln tan open parentheses x over 2 plus straight pi over 2 close parentheses

Answered by  | 26th Apr, 2014, 11:40: AM

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