Is this integral wrong? $$ \int(x^2+1)(x+1)dx$$ Per partes, let $$u = x+1; u' = 1 $$ $$v' = x^2+1; v = x^3/3 + x $$ $$=(x+1)(x^3/3+x) - \int1*(x^3/3+x) = (x+1)(x^3/3+x) - \frac{1}{3}\frac{x^4}{4}-\frac{x^2}{2} + C $$ Wolfram gave me this $x^4/4+x^3/3+x^2/2+x+C$. I understand it, but I would like to know if my solution is right too? (Will I get points for my solution on exam? I know it depends on professor, but does my solution contain any essential mistake?) EDIT: sorry for bad sign, I have badly rewritten it from papers

You are making this a lot harder than it needs to be. Just use the distributive property to expand it out into a polynomial. That is:

$$(x^2 + 1)(x + 1)=x^3+x^2+x+1$$

If you are masochist, however, integration by parts works too. :)