Question

integrate sen(x).cos^2(x)dx. thanks in advance

Answer 1

\[-\frac{ 1 }{ 3 }\cos ^3x\]

Answer 2

i know the answer. what i'm in doubt is about how to reach it. anyway, thank you mhmdrz91.

Answer 3

So for this you might notice that you have the derivative of something multiplied by it, which allows you to do substitution. It will take a little practice to become familiar with it, but after a short while it will be almost obvious.

Try using the substitution u=cosx. I'll help you along the way.

Answer 4

i've already done it. u=\[\cos ^{2} x\], and i got \[du=-2\cos x.\sin x\], \[-du/2= \cos x.\sin x\] it's wrong, isn't it? because you can't reach the right result with this du, i think.

Answer 5

put cos^x = z
diff both sides ,
-sinxdx=dz
put dat in your equation,
\[\int\limits_{}^{}z ^{2}dz\]
dat equals \[-z ^{3}\div3 + c\]
put d value of z ..

Answer 6

I already suggested u=cosx. If one substitution doesn't work, try to figure out why, since it obviously looks very close it might be very similar. So like I said, cosx. It's not cos^2x.

Answer 7

sorry its only cosx=z
and the answer will be -(1/3)cos^3x +c

Answer 8

I think we all 4 of us know what the answer is.

Answer 9

ya and i solved it .

Answer 10

Want a cookie?

Answer 11

why not ??

Answer 12

yes, i noticed it now. the fact is that i'm really sleepy and i have an exam of calc 1 today in a few hours (and studied nothing)...

Answer 13

Sure, ask me anything and I'll tell you anything you need to know and explain it in the best possible way I can so that hopefully it just "makes sense" and you don't have to memorize it.

Answer 14

\[\int\limits_{}^{}e ^{x ^{3}}dx\]
@Kainui

Answer 15

Lol go away kid.

Answer 16

haha ... solve it ...!!

Answer 17

x^3 is the u, no?

Answer 18

http://www.wolframalpha.com/input/?i=e%5Ex%5E3dx&t=crmtb01
There you go, now go away, I'm trying to actually help here not show off.

Answer 19

Don't read what he puts, it's actually a really hard integral similar to the Gaussian. It's not worth your time. @JGMach

Answer 20

ya m sorry ...!!

Answer 21

kainui, i was goig to ask you to solve a two integrals that i had a great doubt on how to solve them, but i took so long typing that i solved both in the middle of the process. the virtual keyboard is really a pellet to use. i need to buy a new one urgently!

ps: sorry for my bad english

Answer 22

i have another one here. how do i solve \[\int\limits \cos [\ln (x)]/(x.\sin [\ln(x)])dx\]?

Answer 23

@Kainui