How do you find the indefinite integral of #int (x^4+x-4)/(x^2+2)#?

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Answer 1 · 2018-04-13T07:50:33

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

We need

#int(u'(x)dx)/(u(x))=ln(u(x))+C#

Perform a polynomial long division

#(x^4+x-4)/(x^2+2)=x^2-2+(x)/(x^2+2)#

Therefore,

#int((x^4+x-4)dx)/(x^2+2)=intx^2dx-int2dx+1/2int(2xdx)/(x^2+2)#

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