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evaluate dx/1+x^4

evaluate dx/1+x^4

Grade:12

1 Answers

vikas askiitian expert
509 Points
10 years ago

I = 1/1+x4 dx

2I =  2/1+x4 dx

divide num & denominator by x2

    =2/x2 /(x2+1/x2) dx

    =[1/x2+1 + 1/x2-1 ]/(x2+1/x2) dx

    =(1/x2+1)dx/x2+1/x2  +  (1/x2-1)dx/(x2+1/x2)

    =(1+1/x2)dx/{(x-1/x)2 + 2} + -(1-1/x2)dx/{(x+1/x)2 - 2}

               I                                          II

put x-1/x = t in first &  x+1/x = u in second & then 

2I =         dt/t2+2                 +          -du/u2-2

2I =         tan-1(t/21/2) / 21/2        +  -log(u-21/2/u+21/2)/81/2 + C

now put  t , u in above eq...

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