Evaluating the integral, correct?

Zack88

[tex]\int \cos^{3}x\sin x dx[/tex]

- cos^4 x / 4

rocomath

Yep. Now look at this problem, but don't pay attention the first part, the 2nd step is what I'm mainly talking about. I spent like an hour evaluating it through Parts a couple times, till I got tired and asked for helped and look how simple it was ...

Zack88

I see how you got to step 3 but not to 4

rocomath

Oh, don't worry about that. I only wanted to emphasize the chain-rule. Step 3 to 4 would take me forever to type, lol.

I simplified a lot to save myself typing-time. I basically used a trig identity.

Zack88

lol i was looking at it and then i tilted my head and was like yep i dont know how that happened

Zack88

woo now i know 6 out of the 18 problems i have to do are correct thanks to you

rocomath

I'm getting sleepy, if you wanna do a couple more better start asking :-]

Zack88

me too me too

[integral] sec^6 x dx

should i do

[integral] (sec^2)^3

or

start doing parts

u= sec^2 x dv = sec^4 x

rocomath

[tex]\int\sec^6 xdx[/tex]

[tex]\int\sec^4 x \sec^2 x dx[/tex]

[tex]\int(\sec^2 x)^2 \sec^2 xdx[/tex]

When you trig identities raised to powers, break it up till you see something.

Zack88

[integral] (tan^2 x +1) sec^2 x dx

u = tan x
du = sec^2 x

[integral] (u^2 =1)^2 du

[integral]u^4 + 2u^2 + 1 du

tan^5 x / 5 + 2tan^3 x / 3 + tan x + c

rocomath

Good!!!

Zack88

woot lol

Zack88

im goin to let my brain cool down for the night, t2ul and have a good night.

rocomath

Alright, I'm going to sleep! You still have Sunday and Monday to finish all 18 problems!!!

Zack88

woo im back, v.v

[integral] sin^5 x cos^3 x

i was wanting to know if i should break it up like

[integral] sin^4 x sin x cos^2 x cos x

rocomath

Look in your book, there should be a suggestion on how to tackle even/odd powers of sines and cosines.

Hint: Leave sin^5 x alone, mess around with cos^3 x

Zack88

[integral] sin^5 x cos^2 x cos x
[integral] sin^5 x (1- sin^2x) cos x

u= sin
du= cos

[integral] u^5(1- u^2) du
[integral] u^5 - u^7 du

1/6 sin^6 x - 1/8 sin^8 x + c