How to solve this: ∫(x^4+1)/(x^2+1)dx ?

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Answer 1 · 2018-01-15T10:55:34

The answer is #=x^3/3-x+2arctanx+C#

#"Reminder"#

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

#intx^ndx=x^(n+1)/(n+1)+C(x!=-1)#

Start by performing a long division

#(x^4+1)/(x^2+1)=(x^2-1)+2/(x^2+1)#

Therefore,

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

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