What is the integration? 1/(2sin x+ cos x +1)

Answers (1)

Solution:  We have ,

              I=int frac12sin x+cos x+1dx

           Put ,     	an (fracx2)=tRightarrow dx=frac21+t^2dt

          \ Rightarrow cos x=(frac1-t^21+t^2);sin x=(frac2t1+t^2)\ \Rightarrow 2sin x+cos x+1=2(frac2t1+t^2)+(frac1-t^21+t^2)+1=frac2(1+2t)1+t^2

       	herefore intfrac1(1+2t)dt=frac12ln(1+2t)+c

     Rightarrow I=frac12ln[1+2	an(fracx2)]+c.  

       

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