Question

integrate x^2/ sqrt(4+x^2)

Answer 1

did you try
u= 4+x^2
?

Answer 2

no, let me do that

Answer 3

cool, let me know if you get stuck on any step :)

Answer 4

another way i could think of is to write

x^2 as
x^2+4-4

and then splitting the fraction

sqrt (x^2+4)-4/sqrt(x^2+4)

Answer 5

du=2xdx and im not sure what to do with the x

Answer 6

x= \sqrt (u-4)
now find dx

Answer 7

my new integral looks like \[\int\limits (u-4)/ 2(\sqrt{u \sqrt{u-4}})\]

Answer 8

xdx=du
you don't need to do anything
you x^2 on top
make it x.xdx

Answer 9

However, this is little different from what @hartnn suggested

Answer 10

so what would u be?

Answer 11

Some other suggestions for substituting: try \(x=2\tan u\) or \(x=\sqrt t\).

Answer 12

oh yeah i like that sub @SithsAndGiggles suggested just now
makes thing a lot simpler
try it^_^

Answer 13

i meant the x=2tanu

Answer 14

this requires some trig identities to do^_^

Answer 15

how do i make x=2tanu?

Answer 16

for u as you started first
u=4+x^2
du=2xdx =====> 1/2du=xdx if you want to continue this way

Answer 17

set x=2tanu
then x^2=4tan^2u