anyone know the answer to the integral of ((x^4)+1)/((x^3)+x) with respect to x?

Answer 1

Use partial fractions then get

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

which is better written as 1/2*x^2 + ln(x) - ln(1+x^2)

Apparently the partial fractions should work out as x + 1/x - 2x/(1+x^2)

Answer 2

(( x^4)+1)/((x^3)+x) = x + (1/x) - 2.x/(x^2 +1), so the integral is:
x^2/2 + ln x - ln((x^2 +1).

Answer 3

integral ((x^4)+1)/((x^3)+x) dx=
integral(x+(-x^2+1)/((x^3+x))dx