How can I simplify this integral with a variable exponent in the denominator?

[renob]

Homework Statement

$$\int(x^4+2x^2+x+1)/(x^2+1)^x$$

The Attempt at a Solution

am I supposed to multiply out the denominator then do u sub?

 

[renob]

nevermind i think its arctan

 

[HallsofIvy]

It isn't anything if the exponent on that denominator is really "x"! If it was supposed to be "2", I recommend dividing the fraction our so that you have a polynomial plus a "proper fraction" of the form $$\frac{ax+ b}{x^2+ 1}$$. That you divide into two parts: $$\frac{ax}{x^2+1}$$ and $$\frac{1}{x^2+ 1}$$. The first uses the simple substitution $$u= x^2+ 1$$ and the second is an arctan.