Question

int sin^5xcos^2x please help :)

Answer 1

Trig sub, let u = ?

Answer 2

duh nuh nuh duh nuh nuh batman!

Answer 3

i know i have to separate the sin^5x

Answer 4

so it would be int sin^4xsinxcos^2x

Answer 5

right?

Answer 6

then would i replace the terms with the trig identities?

Answer 7

reduction formula?

Answer 8

i dunno :( lol

Answer 9

U sub^_^

Answer 10

oh man it's one of the examples in the book :D :D

Answer 11

this must be what heaven feels like... lol

Answer 12

first rewrite cos^5x using trig identities

Answer 13

\[\int\limits \sin ^{5}x \cos ^{2}x dx=\int\limits \sin ^{4}x sinx cosx dx\]

Answer 14

\[u=cosx\]\[du=-sinx dx\]\[-\int\limits \sin ^{4}xu ^{2}du=-\int\limits (1-u ^{2})^{2}u ^{2}du=-\int\limits (u ^{2}-2u ^{4}+u ^{6})du\]

Answer 15

I think I did it right

Answer 16

yeah you did :)

Answer 17

oh something is wrong?

Answer 18

hm?

Answer 19

i would choose u=sinx
du=cosxdx

Answer 20

u^4=sin^4x

Answer 21

the book went with u=cosx

Answer 22

why?

Answer 23

so int(u^4udu)=int(u^5du)

Answer 24

but it made everything all negative to fix for it

Answer 25

no no need for that mess
realize that cosxdx is du
that's wat you need to observe
so we need to me u=sinx then du=cosxdx

Answer 26

oh hold on it should be cos^2x not cosx
lol

Answer 27

yeah i think that's why it picked cos as u

Answer 28

so then it could make u^2 etc

Answer 29

as opposed to du^2

Answer 30

I'm wrong! i went with cosx not cos^2x
his solution is correct

Answer 31

calc is friggin hard man it hurts my brain

Answer 32

calc 1 was so easy and then this crap

Answer 33

eh cal2 isn't really that hard, just some attention
all there is to it some trig, partial fraction and some other techniques
meaning basically dealing with algebra rather than calculus

Answer 34

yeah its the trig thats killing me

Answer 35

if you got cal1 story you won't have problem with this Calc

Answer 36

all that fiddling and wiggling crap around trying to make it fit. it's like theres almost no structure to it it always depends on what it is and you gotta fiddle with it

Answer 37

Most students face algebra problem rather than calc
namely trig

Answer 38

<3 algebra. there are so many rules and they're always the same. but with trig it always depends and that kills me

Answer 39

yeah! well you are excepted to have good knowledge on trigs already
all they do is form some composition of trig functions and logs exponential
and also polynomials

Answer 40

or sometimes product of those six functions!

Answer 41

well you might want to check trig again see the identities to reconnect things
because there is no helping it without it! I acually don't remember all trig stuff lol
namely secx cscx, cotx! when i studied trig and calc we never paid attention to those
but at any rate one can always derive things once you know how to handle cosx sinx

Answer 42

I am doing calc3 which is multi stuff and that is really painful