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answered 2012-01-21 18:04:48 +0100
sage: var('x,a,b')
sage: integrate(1/sqrt(b+a/x), x,algorithm='mathematica_free')
sqrt(b + a/x)x/b - 1/2alog(2sqrt(b + a/x)sqrt(b)x + 2bx + a)/b^(3/2)