#intsqrt(x+2) -1/(sqrt(x+2)) +1# ?

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Answer 1 · 2018-07-02T14:33:55

The answer is #=2/3(x-1)(x+2)^(1/2)+x+C#

The integral is

#I=int(sqrt(x+2)-1/sqrt(x+2)+1)dx#

#=intsqrt(x+2)dx-int(1dx)/sqrt(x+2)+int1dx#

#=int(x+2)^(1/2)dx-int(x+2)^(-1/2)dx+int1dx#

#=(x+2)^(1/2+1)/(1/2+1)-(x+2)^(-1/2+1)/(-1/2+1)+x+C#

#=2/3(x+2)^(3/2)-2(x+2)^(1/2)+x+C#

#=(x+2)^(1/2)(2/3(x+2)-2)+x+C#

#=(x+2)^(1/2)(2/3x-2/3)+x+C#

#=2/3(x-1)(x+2)^(1/2)+x+C#