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Integrate: x/(1+x tan x)

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Solution:  We have ,   

                 I=int fracx1+x an xdx

       \Rightarrow I=int fracxcos xcos x+ xsin xdx           Put    (cos x+xsin x)=tRightarrow xcos xhspace0.1cmdx=dt

          herefore     I=int (frac1t)dt=lnleft | t ight |+c=lnleft | cos x+xsin x ight |+c 

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Deependra Verma

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