I have to integrate cos^2(x). Wolfram tells me that I will have to write cos^2(x) as (cos2(x)+1)/2 to proceed. Why is that? Isn't there a direct method of integrating trigonometric functions that have powers? If yes, why? :)

Question

amistre64 · Answer

potatoe potatoe

anonymous · Answer

That didn't help.

amistre64 · Answer

its more effective when read in context :)  its 2 different ways of getting to the same results

amistre64 · Answer

i say potatoe, you say potatoe ....

amistre64 · Answer

the reduction formula is the "direct" method

amistre64 · Answer

lets see if i can recall it correctly:$$\int cos^n=\frac{1}{n}cos^{n-1}sin+\frac{n-1}{n}\int cos^{n-2}$$

anonymous · Answer

Which method is more intuitive? I have opened an MIT lecture about power reduction on another tab, by the way.

amistre64 · Answer

cos^2 is small enough that rewriting it in its identity tends to be simpler than trying to recall the formula

amistre64 · Answer

the intergral of cos^n is by parts; whereas cos^2 is just an identity