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int(sqrt(1+x^2))/(x^4) dx...

`int(sqrt(1+x^2))/(x^4) dx`

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Let `I = int(sqrt(1+x^(2)))/(x^(4))dx = int(sqrt(1+x^(2)))/(x).1/(x^(3))dx`
` = intsqrt((1+x^(2))/(x^(2))).(1)/(x^(3))dx = intsqrt((1)/(x^(2))+1).(1)/(x^(3))dx`
Put `1+(1)/(x^(2))=t^(2) rArr (-2)/(x^(3))dx = 2t dt`
`rArr -(1)/(x^(3)) =t dt`
`:. I = -int^(2)dt = - (t^(3))/(3) + C = - (1)/(3)(1+(1)/(x^(2)))^(3//2) + C`
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