## 1018 one year ago integrate cos^2(x) dx

1. UnkleRhaukus

$\int\cos^2x\,\mathrm dx = \int\frac{1+\cos2x}{2}\,\mathrm dx \\ \hspace{5em}= \frac12\int\,\mathrm dx +\frac12\int\cos2x\,\mathrm dx\\ \hspace{5em}=$

2. 1018

hey thanks! but can you explain the first part? how did that become a fraction? is that a formula?

3. 1018

oh and also please the whole of it. haha. the 1 + and then if i should always bring down the exponent

4. 1018

thanks

5. UnkleRhaukus

from $\cos(a)\cos(b)= \frac12\Big[\cos(a-b)+\cos(a+b)\Big]$ where, $$a=b=x$$ $\cos(x)\cos(x)= \frac12\Big[\cos(x-x)+\cos(x+x)\Big]$ $\cos^2(x)= \frac12\Big[1+\cos(2x)\Big]$

6. UnkleRhaukus

its probable a good idea to bring down the exponent with the 'Power Reducing Formula', (that i still have to look up every time) there might be another way

7. UnkleRhaukus

*probably

8. 1018

ok, i think i got it. i also looked up the power reducing formula. thanks!