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`        integrate x^2/(x^2+1)*(x^2+4) dx`
8 years ago

```							I = x2/(x2+1)(x2+4) dx
let x2 = t then
x2/(x2+1)(x2+4) = t/(t+1)(t+4)
now using partial fraction
t/(t+1)(t+4) = A/(t+1) + B/(t+4)
A,B = -1/3 , 4/3
t/(t+1)(t+4) = -1/3(t+1) + 4/3(t+4)
again replacing t by x2
I  = [-1/3(x2+1) + 4/3(x2+4) ]dx                                             [ 1/x2+a2 dx = tan-1(x/a)/a ]
I = [ -tan-1x]/3 + 2tan-1(x/2)/3 ] + C
approve my ans if u like
```
8 years ago
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