How do you integrate #int (x^4)/(x^(5)+1) #?

Question

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Answer 1 · 2015-05-05T18:29:51

#int(x^4dx)/(x^5+1)=1/5ln(x^5+1) +C#

Method

#int(x^4dx)/(x^5+1)= 1/5int(5x^4dx)/(x^5+1)= 1/5int(d(x^5+1))/(x^5+1)= " I"#

NB: #d(x^5+1)# simply means that the derivative of #x^5+1# is #5x^4#

Now, you could as well let #u=x^5+1#

So that,

#"I"=1/5int(du)/u=1/5lnu=1/5ln(x^5+1) +C#