What is the possible approach to integrate this?

Question

anonymous · Answer

$$\int\limits_{ }^{ }\frac{ (x ^{2}+x+1) }{ \sqrt[4]{(x^{2}+1} }dx$$

amistre64 · Answer

by parts

anonymous · Answer

hmm, what is my u? dv?

amistre64 · Answer

at first thought, the poly would derive leaving the rest of it to integrate up

amistre64 · Answer

but without an 2x to play with that might not be feasible

amistre64 · Answer

if we rationalize the denominator  ...  could that work out any better?

amistre64 · Answer

$$\int\limits_{ }^{ }\frac{ (x ^{2}+x+1) }{ \sqrt[4]{(x^{2}+1)} }dx$$
$$\int\limits_{ }^{ }\frac{(x ^{2}+x+1)~(x^2+1)^{3/4}}{x^2+1}dx$$

anonymous · Answer

multiplying denominator by itself, including numerator... would it complicate further the equation?

amistre64 · Answer

it might ....

amistre64 · Answer

u = x^2 + 1
du = 2x dx

$$\int\frac{ 2x(u+x) }{ \sqrt[4]{u} }du$$

lol

anonymous · Answer

try to work on this afterwards... got to work first... thanks for the assistance... :)

amistre64 · Answer

anonymous · Answer

yup, i've seen your link... thanks again for your help... :)