Question

Find the indefinite integral.

Answer 1

\[\int\limits\frac{ \arcsin2x }{ \sqrt{1-4x^2} }dx\]

Answer 2

isn't the derivative of the numerator the denominator?

Answer 3

Is it? >_<

Answer 4

got stuck sorry

Answer 5

make a u substitution
\[u=\arcsin(2x), du =\frac{2}{\sqrt{1-4x^2}}\] and you are mostly done

Answer 6

It's okay! Ironically, I was just going to seperate that integral and and go from there. :x

Answer 7

always a bad idea

Answer 8

>_< Really?

Answer 9

I don't know, I guess I don't really get it. :(

Answer 10

do you get the answer to this?

Answer 11

you have a function times its derivative, so the integral is easy

Answer 12

No, I mean... the only thing I had noticed so far was that it looks like the the integral for arcsin. I mean the bottom does, so I recognize that...

Answer 13

you mean the derivative of arcsine

Answer 14

Or would it be as simple as just.... setting dx = du...

Answer 15

you should get
\[\frac{1}{4}\left(\arcsin(2x)\right)^2\] instantly in your head
and to see that it is correct, take the derivative and get what you started with

Answer 16

you got that or you want to go slow and do it step by step?

Answer 17

Whichever way is less complicated. :/

Answer 18

ok you recognize that the derivative of \[\arcsin(2x)\] is
\[\frac{2}{\sqrt{1-4x^2}}\] right? you need to basically know that at the start, otherwise you cannot do the problem, so i will assume that you know it

Answer 19

Oh.... yeah. Had to pull up the rule sheet. :)

Answer 20

once you know that you write the following
\[u=\arcsin(2x), du =\frac{2}{\sqrt{1-4x^2}}dx,\frac{1}{2}du=\frac{1}{\sqrt{1-4x^2}}dx\] and your integral becomes the simple
\[\frac{1}{2}\int udu\]

Answer 21

anti derivative is
\[\frac{1}{4}u^2\] sustitite back and get
\[\frac{1}{4}(\arcsin(2x))^2\]

Answer 22

how we doing @fate?

Answer 23

I kind of understand. I'm sure as I see more problems and try to work through them, this will make more sense. :) Practice makes perfect, right?

Answer 24

i spose

Answer 25

i find this stuff less interesting that eating plain rice crackers and drinking luke warm water

Answer 26

Lol.