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Answer 1 · 2017-05-07T22:12:36

#int_1^4 6x/sqrtx+4/sqrtx \ dx#

#= int_1^4 6sqrtx+4/sqrtx \ dx#

#= int_1^4 6(x)^(1/2)+4(x)^(-1/2) \ dx#

#= [ 6x^(1/2+1)/(1/2+1)+4x^(-1/2+1)/(-1/2+1) ]_1^4#

#= [ 6x^(3/2)/(3/2)+4x^(1/2)/(1/2) ]_1^4#

#= [ 4x^(3/2)+8x^(1/2) ]_1^4#

#= [ 4x^(1/2) (x + 2) ]_1^4#

#= [ 4(4)^(1/2) (4 + 2) ] - [ 4(1)^(1/2) (1 + 2) ] #

#= 48 - 12 = 36#