How do anti-differentiate this?

integral of (sin^3 x)

I'm pretty sure this is wrong, but I got "-x + (cos^3x)/3"

I don't think that x should be hanging around there :S For odd powers of sin, you have to use a certain subtitution... I forget what though. And then you use a diff one for even powers.

This is what I don't understand of Math. Where does the fucking ^3 go? It sure doesn't power the function, but the value of the function, so what the fuck. And why are you fucking with parenthesis. This should have been sin(x)^3 , as any rational person would have written. (sin^3 x) is uglier than my grandma's butt. I think Math syntax was designed by the same guy who did Perl.

I concur #3. But, sadly, IB (a world renowned international faggot organization) wrote it as sin^3 x on their exam, so I just copied what they did.

Break it up into sin(x)*(sin(x))^2

then use power reduction on the squared part and then use the product rule.

and by product rule, I mean integration by parts(or, I haven't worked this out, if it works out nicely enough to do a simple u substitution do that)

Actually fuck that shit, I just worked it out and you don't need integration by parts

all you have to do, if it is actually sin^3(x)
is break it into sin(x)*sin^2(x) and then use power reduction on the sin^2(x) which becomes (1 -cos(2x))/2 or some shit and then the integration is very basic

The reason the ^3 is in the middle is so it is not interpreted as the sine of x-cubed.

Meanwhile, sin^-1 is arcsin.

>>9
Yeah, this is awesome, it really looks like a Perl hack.

>>8
That's what parenthesis are for BTW. Why don't they fucking write the fucking parenthesis for trigonometric functions while they do for f(x)? Being a lazy fucktard about them led to powering function names instead of function values, then it led to wrapping all functions around parenthesis if they're in a larger expression, like (sin^3 x). Retarded.

Another thing I don't like is how they ommit the product operator. How can I tell if arcsin x is arcsin of x or a*r*c*sin of x?

Oh and this stupidity brought yet another problem. Because of something as retarded as omitting *, so they can write 3f(x) and fap to it because it's so cool, they made all variables one character. This is lame.

>>7 sin^2(x) which becomes (1 -cos(2x))/2

It becomes integral sinx(1-cos^(2)x) dx
Then sub in u for cosx and it simplifies into: integral -1 + u^2

-x + u^(3)/3
-x + (cos^3x)/3

I think...

http://en.wikipedia.org/wiki/List_of_integrals_of_trigonometric_functions

Second formula.

[-cos^4 (x)]/4

if you differentiate that you should get sin^3 (x)
i'm pretty sure. then again i just started this chapter too.

>>15
wrong. go back to calc II.

-sin^2(x)cos(x)/3 - 2cos(x)/3 + C