Question

integrate cos^2(x) dx

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

thanks

Answer 5

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

Answer 6

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

Answer 7

*probably

Answer 8

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