$\int\frac{x^2+x+1}{x^5+2x^4+x^3}dx$
$-x^2+4x-2$
$16x^4+24x^2+9x$
$\frac{x^2-2x+1}{1-x}$
$\int_0^{\frac{\pi}{3}}sec^4x\:dx$
$x\left(1+x\right)^{-\frac{5}{2}}$
$4x^4+24x+36$
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