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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