int (x^(1/4))/(1+x^(1/2))

Question

chaise · Answer

$$\int\limits \frac{x ^{\frac{1}{4}}}{1+x^{\frac{1}{2}}}$$

Is this what you're asking? Do you just want an answer, or how to solve?

anonymous · Answer

yes that is what I am asking. I would like to know how to solve the problem.

anonymous · Answer

hmm, I feel that this looks a lot like, u / (1+u^2), where u = x^(1/4).  Perhaps such a substitution would help?

anonymous · Answer

put 
$$u= x^{\frac 1 4}
$$
afer simplification, you get
$$
4 \int \frac { u^4}{u^2 +2}du 
$$
and continue after that

anonymous · Answer

Got it now thank you.

anonymous · Answer

cool.  and remember to mark the question as closed once you have solved it.  thanks!

anonymous · Answer

done.

anonymous · Answer

Notice that
$$
\frac{u^4}{u^2+1}=u^2-1 +\frac{1}{u^2+1}
$$
Now it is easy.

anonymous · Answer

After integrating and replacing you get
$$
\frac{4 x^{3/4}}{3}-4
   \sqrt[4]{x}+4 \tan
   ^{-1}\left(\sqrt[4]{x}\right) + C
$$