How to evaluate $\int \frac {x^3} {1+x^6} dx $?

Question

How to evaluate $\int \dfrac {x^3} {1+x^6} dx $ ? I am completely at a loss , please help , thanks in advance .

Answer 1

HINT:

Set $x^2=y$

$$\int\dfrac{x^3}{1+x^6}dx=\int\dfrac y{1+y^3}\cdot\dfrac{dy}2$$

Now use partial fraction decomposition $$\dfrac y{1+y^3}=\dfrac A{1+y}+\dfrac{By+C}{1-y+y^2}$$