Question

Integral question

Answer 1

@inkyvoyd

Answer 2

I know the substitution formula and how to get U and DU, so on so fourth.

Answer 3

So where we getting stuck?
Let u equal the stuff up in the exponent.
Ooo this one works out nicely I think!

Answer 4

\[\LARGE\rm \int\limits t^{15}e^{-t^8}dt=\int\limits t^{8+7}e^{-t^8}dt\]\[\Large\rm =\int\limits t^8 e^{-t^8}\left(t^7~dt\right)\]If you break it up like this, it might be easier to plug in your substitution.

Answer 5

\(\Large\rm u=-t^8\)
\(\Large\rm du=-8\left(t^7~dt\right)\)Can you kinda see what's going on?

Answer 6

Hmm yes I like how you broke it up.

Answer 7

Well, I thought I was getting it.

Just me, I was doing

U=t^15
DU=15t^14

DV=e^-t8

Answer 8

So you were trying to jump right into the `integrating by parts` before doing a substitution.
See how that runs into trouble?
Finding your V would be impossible without borrowing some of those t's from the U.

Answer 9

Confused still senor bus? :U

Answer 10

Oh goodness. It does help to read instructions!
Forgive me zepdrix. Thanks for your patience and help! My AmTran is tired lol. Onward!

Answer 11

So the substitution is basically breaking up the 15?

Answer 12

I'll call it something else, not u, so there's no confusion that this has nothing to do with integration by parts.
\[\Large\rm \color{orangered}{m=-t^8}\qquad\to\qquad \color{royalblue}{-m=t^8}\]\[\Large\rm \color{green}{-\frac{1}{8}dm=\left(t^7~dt\right)}\]Yah, we're breaking up the 15,
and applying a substitution before even assigning any parts.\[\Large\rm =\int\limits\limits \color{orangered}{t^8} e^{\color{royalblue}{-t^8}}\color{green}{\left(t^7~dt\right)}\]

Answer 13

Bahh I got the orange and blue backwards.. my bad :P

Answer 14

Thats fine! The m makes sense!

Answer 15

\[\Large\rm =\frac{1}{8}\int\limits m e^m~dm\]So before applying our parts, we have ummm something like this, yes?

Answer 16

And I'll bet you can handle the parts from there c:
Shouldn't be too bad.

Answer 17

I'll try!

Answer 18

http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427ed8at9flt29

Answer 19

This gives a foundation to work with.