Question #64159

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Answer 1 · 2017-04-17T13:48:05

#int(x+1/x)^2dx#

Expand the square:

#=int(x+1/x)(x+1/x)dx#

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

#=int(x^2+2+x^-2)dx#

Integrate these using #intx^ndx=x^(n+1)/(n+1)# and #aintdx=ax#:

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

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

Getting a common denominator:

#=(x^4+6x^2-3)/(3x)+C#