Integrate: 1 / x(1+x^4)

Answers (1)

Solution:

          I=int frac1x(1+x^4)dx\ \ Rightarrow hspace1cmI=int frac1x^5(frac1x^4+1)dxhspace1cmLet hspace1cm frac1x^4+1=t\ \ Rightarrow hspace1cm-frac4x^5dx=dt \ \ Rightarrow hspace1cmI=-frac14int frac1tdt=-frac14ln left | t 
ight |+c \ \ Rightarrow hspace1cmI=-frac14ln left | frac1x^4+1 
ight |+c

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