$$y=x^4+1$$
1) factorise y
2) find $$\int \frac{1}{x^4+1} dx$$

Question

$$y=x^4+1$$
1) factorise y
2) find $$\int \frac{1}{x^4+1} dx$$

zepdrix · Answer

Hmm we have the sum of squares.
So I guess we want to break this into complex conjugates yes?
You've learned about complex numbers I assume? :o

anonymous · Answer

These kind of problems should not be done by hand anymore. We should teach our students how to use integrals to solve real life problems and not to ask them to spend time on endless computations that can be done neatly and fast by a machine.
Here what mathematica gave
$$
\int \frac{1}{x^4+1} \, dx\=\frac{\log \left(x^2+\sqrt{2} x+1\right)-\log \left(x^2-\sqrt{2} x+1\right)+2
   \tan ^{-1}\left(\sqrt{2} x+1\right)-2 \tan ^{-1}\left(1-\sqrt{2} x\right)}{4 \sqrt{2}} + C
$$