Question

integral of (1 + cos x)^2

Answer 1

i guess you have to square it and take
\[\int(1+2\cos(x)+\cos^2(x))dx\]

Answer 2

\[x+2\sin(x)+\int\limits_{}^{}\frac{1}{2}(1+\cos(2x)) dx +C\]

Answer 3

first to are rather simple and for the second one use
\[\cos^2(x)=\frac{1}{2}\cos(2x)+\frac{1}{2}\]

Answer 4

a standard trick for
\[\cos^2(x)\] so standard that i might be worth memorizing

Answer 5

i bet myininaya has it memorized for sure right?

Answer 6

or you could use cos(x+x)=cos(x)cos(x)-sin(x)sin(x) and
sin^2(x)+cos^2(x)=1
to derive it

Answer 7

sure if you had an infinite amount of time

Answer 8

lol it doesn't take long

Answer 9

but since it never changes might as well learn it at least until calc class is over. kind of like knowing that
\[7\times 8=56\] or that
\[\int\ln(x)dx=x\ln(x)-x\]