evalute int [ from (0) to( pi)] {1/t-cosx}dx t>0

                   evalute           int [ from (0) to( pi)]  {1/t-cosx}dx     t>0  


1 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago


Dear Baha, 

I= int(0 to pi){1/(t-cosx)}dx, let tan(x/2)=s, dx= 2ds/(1+s2),I=∫(0 to infinity)2ds/((1+s2)(t-cosx)==∫(0 to infinity)2ds/((1+s2)t+s2-1)=

(2/(t+1))∫(0 to infinity)ds/(s2+((t-1)/(t+1)))=(2/(t+1))[√((t+1)/(t-1))(arctan(s√((t+1)/(t-1))¦0infinity = π/√(t2-1)

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