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```        please help me to solve:
1) integral 2X *X / (X *X +1)(X *X +1)   dx
2)  integral dx/( X *X*X*X+X *X +2)```
6 years ago

510 Points
```										1)        2x2/(x2+1)2 dx
=  [2(x2+1) - 2]dx/(x2+1)2
=[2/(x2+1) - 2/(x2+1)2]dx
I = 2tan-1x - 2dx/(x2+1)2
I - 2tan-1x = -2dx /(x2+1)2       .........................1
taking RHS
put x = tan@ so
dx = sec2@d@
now
RHS = -2d@/sec2@  =  -2cos2@ = -(1+cos2@)d@
=-(@ + sin2@ /2) + c
=- [ tan-1x + sin(2tan-1x)/2] + c
put RHS in eq 1 then
I = tan-1x - sin(2tan-1x) / 2  + c    or
I = tan-1x -  x/1+x2  +  c
```
6 years ago
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