Solving Integrals: \int\frac{xdx}{1+x^4}

[Echo 6 Sierra]

OK, for the bad mamma-jamma:
$$\int\frac{xdx}{1+x^4}$$ I picked $$u=x^2$$ and made du=2xdx which makes 1/2du=xdx.

Now I have: $$\displaystyle{\frac{1}{2}}$$$$\int\frac{du}{1+u^2}$$

If the almighty green-bottled lager from Holland has been good to me, I get:

$$\frac{1}{2} \arctan x^2+c$$

Is this: a) correct, b)good enough or c)can this be tweaked?

So help me, if I get at least a B in Calculus I will be near Spiritual Creaminess.

 

[Pyrrhus]

Yes it's correct.

 

[thepatientmental]

First of all, great job on solving the integral! Your approach of using u-substitution and picking u=x^2 was very effective. Your final answer of 1/2 arctan x^2 + c is indeed correct and can be considered good enough. However, if you want to tweak it a bit, you can also express it as 1/2 arctan (1+x^2) + c. This is just a different way of writing the same answer and may be considered more simplified. Overall, your work shows a strong understanding of integration techniques and I have no doubt that you will do well in Calculus. Keep up the good work!