Taylor Series
Using known Taylor series, find the first four nonzero temrs of the Taylor sieries about 0.

arcsin x

1. I found it's derivative to be 1/1-x^2
2. I know the Taylor series for 1/1-x
1+x+x^2+x^3+...
3. So I substituted in x^2 for x in the taylor series and got
1+x^2+x^4+x^6+...
4. Then I integrated the series and got
x+x^3/3+x^5/5+x^7/7+...
but the answer is
x+(1/6)x^3+(3/40)x^5+(5/112)x^7+...

Any idea what I did wrong?

Question

Taylor Series
Using known Taylor series, find the first four nonzero temrs of the Taylor sieries about 0.

arcsin x

1. I found it's derivative to be 1/1-x^2
2. I know the Taylor series for 1/1-x
1+x+x^2+x^3+...
3. So I substituted in x^2 for x in the taylor series and got
1+x^2+x^4+x^6+...
4. Then I integrated the series and got
x+x^3/3+x^5/5+x^7/7+...
but the answer is
x+(1/6)x^3+(3/40)x^5+(5/112)x^7+...

Any idea what I did wrong?