integrate x^5/(x^2 + sqrt(2)) using a table of integrals

Answer 1

Let X = a + bx + c x^2, with a = sqrt2, b = 0 and c = 1.

The integral of x^5/X is
x^4/4 - sqrt2*(Integral of x^3 dx/X)

Use the recursion formula again for the second term.

The integral of x^3/X is
x^2/2 - sqrt2*(Integral of x dx/X)

The Integral of x dx/X is
(1/2)ln X = (1/2)ln(sqrt2 + x^2)