How do you integrate sqrt( (x^2) +1) ) / (x^2)? I know the answer but my book

UnsexMe

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doesn't show the steps...? the answer is ( -sqrt( (x^2) + 1) / x ) + ln ( x + sqrt( (x^2) +1) ) + C...
I think you do integration by parts where u = sqrt( (x^2) + 1) and dv = du/ (u^2) and du = (2u / 2 sqrt( (x^2) + 1) ) and v = - 1/ u. However, when I go through with the integration I can only get the first term of the answer... What am I doing wrong??
 
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