Question

Integrate...

Answer 1

\[\int\limits r^3 \sqrt{4r^2+1}\ dr\]Wolfram Alpha shows a solution with multiple substitutions, but I can't really follow what it's doing. I'm not sure what approach to use for this integral. Integration by parts?

Answer 2

did u try 4r^2 +1 = u ?

Answer 3

\[dr = \frac{du}{8r}\]

Answer 4

r^3 dr = r^2 (rdr) = (u-1)/4 (du/8)

Answer 5

Ah... Let me try that.

Answer 6

OK, yeah. That works out just fine. Why try that substitution?

Answer 7

magic