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This result is similar to that from W-alpha:

sage: integrate((a/x+b*x^c)^d,x,algorithm='mathematica_free')

-(x^cb + a/x)^dx*hypergeometric2f1(-(d - 1)/(c + 1), -d, -(d - 1)/(c + 1) + 1,

-bx^(c + 1)/a)/((d - 1)(b*x^(c + 1)/a + 1)^d)

This result is similar to that from W-alpha:

sage: integrate((a/x+b*x^c)^d,x,algorithm='mathematica_free')integrate((a/x+b*x^c)^d,x,algorithm='mathematica_free') -(x^cb -(x^c*b + a/x)^dx*hypergeometric2f1(-(d a/x)^d*x*hypergeometric2f1(-(d - 1)/(c + 1), -d, -(d - 1)/(c + 1) + 1, -bx^(c -b*x^(c + 1)/a)/((d - 1)(b*x^(c 1)*(b*x^(c + 1)/a + 1)^d)1)^d)