Integrate: (x + sin x)/(1+cos x)

Answers (1)

Solution: We have ,

                 I=int fracx+sin x1+cos xhspace0.2cmdx

        \ Rightarrow I=int fracx+2sin fracx2cdot cos fracx22cos^2(fracx2)hspace0.2cmdx\ \Rightarrow I=int [frac12xsec^2(fracx2)+	an (fracx2)]hspace0.2cmdx

        Put ,   fracx2=tRightarrow (frac12)dx=dt

       \Rightarrow I= 2int [tsec^2t+	an t] dt

     	herefore     I=2[t	an t-int 	an t hspace0.2cmdt+int 	an thspace0.2cmdt]\ \ Rightarrow I=2t 	an t+c=x	an (fracx2)+c.

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