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`        evaluate dx/1+x^4`
6 years ago

510 Points
```										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...
```
6 years ago
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