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#### Pindrought

##### New member

- Mar 3, 2014

- 15

\(\displaystyle \int \frac{x^2}{\sqrt{4 - x^2}} \, dx\)

I do a substitution and set

\(\displaystyle x={\sqrt{4}}sinu\)

I get to this step fine

\(\displaystyle \int 4sin(u)^2\)

I know that u = arcsin(x/2)

so I don't see why I can't just substitute in u into sin(u)?

I tried this and I got

\(\displaystyle \int 4 * arcsin(sin(x/2))^2\)

which worked out to

\(\displaystyle \int 4 * \frac{x^2}{4}\)

which gave me

\(\displaystyle \int x^2\)

which would just mean the answer is

\(\displaystyle \frac{x^3}{3}\)

But looking at the mathhelpboards solver, this is wrong. Can anyone help me figure out what I am not understanding? Thanks a lot for taking the time to read.