> int(1/(x^5-x^4+x^3-x^2+x-1),x);

1/3*ln(x-1)-1/3*sqrt(3)*arctan(1/3*(2*x-1)*sqrt(3))...

> factor(x^5-x^4+x^3-x^2+x-1);

(x-1)*(x^2+x+1)*(x^2-x+1)

> convert(1/(x^5-x^4+x^3-x^2+x-1),parfrac,x);

1/3*1/(x-1)-1/6*(1+2*x)/(x^2+x+1)-1/2*1/(x^2-x+1)

> int(1/(x^2+2),x);

1/2*sqrt(2)*arctan(1/2*x*sqrt(2))

> diff(arctan(x),x);

1/(1+x^2)

>