Question

\[\int\limits \sqrt(x) / (1+ x^.25) \]

Answer 1

\[\int\sqrt{\frac{x}{1+x^{1/4}}}~dx~~?\]
or
\[\int\frac{\sqrt x}{1+x^{1/4}}~dx~~?\]

Answer 2

the 2nd one!

Answer 3

Notice that \(\left(x^{1/4}\right)^2=x^{2/4}=x^{1/2}=\sqrt x\).

So if you let \(u=x^{1/4}\), so that \(u^2=x^{1/2}\).

Differentiating, you get \(du=\dfrac{1}{4}x^{-3/4}~dx\), or \(4x^{3/4}~du=dx\), or \(4u^3~du=dx\).

So the integral becomes
\[\int\frac{u^2}{1+u}~(4u^3~du)\\
4\int\frac{u^5}{1+u}~du\]

Answer 4

Thank you, I see now where I messed up the problem! Appreciate your help

Answer 5

You're welcome!