How to integrate r³√(r²+1)

[J Goodrich]

How does one compute

$$\int r^{3}\:\sqrt{r^{2}+1}\:dr$$

Does this involve double u sub or trig sub?

Thanks in advance,
Justin

 

[tiny-tim]

Hi Justin!

(have a square-root: √ and an integral : ∫ and try using the X² tag just above the Reply box )

trig sub is probably easiest.

(alternative hint: write it ∫ r(r²)(r² + 1)^1/2 dr )

 

[HallsofIvy]

I would think the second was easiest: Let $u= r^2+ 1$. Then du= 2rdr and $r^2= u- 1$. (A single u-substitution, not double.)