Find the intergral of the following:-

Asked by uma.therighter | 13th Jun, 2009, 08:52: AM

Expert Answer:

1/(1-tanx) =cosx/(cosx-sinx) =1/2  (   1+ (sinx+cosx)(cosx-sinx) )

Now I= 1/2  (   1+ (sinx+cosx)(cosx-sinx) )dx=x/2 +1/2    (sinx+cosx)(cosx-sinx)  dx

Put -sinx+cosx=t in the second term,

1/2    (sinx+cosx)(-sinx+cosx)  dx=1/2     -dt/t = -1/2lnt

Hence I=x/2-1/2ln(-sinx+cosx) +c

 

Answered by  | 13th Jun, 2009, 06:48: PM

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