## AmTran_Bus one year ago Integration help

1. anonymous

?

2. AmTran_Bus

|dw:1434926190793:dw|

3. triciaal

products

4. AmTran_Bus

|dw:1434926209378:dw|

5. AmTran_Bus

$uv-\int\limits vdu$

6. idku

more steps, but less mess and confusion. u=-3t then by parts

7. AmTran_Bus

$t \frac{ e ^{-3t} }{ 3 }-\int\limits \frac{ e ^{-3t} }{ 3 }dt$

8. idku

u can do a power series too, if you would like.

9. idku

anyway, u got people here....

10. AmTran_Bus

This is what I'm doing right now, this is the IBP section.

11. AmTran_Bus

So do a U sub first? ok.

12. idku

yes, u=-3t

13. idku

du=(-3)dx -> du/(-3) = dx

14. idku

u got this:)

15. idku

(don't forget to sub back the x)

16. AmTran_Bus

So do I need to say dt = -du/3?

17. idku

yes that suffices

18. AmTran_Bus

|dw:1434926595047:dw|

19. AmTran_Bus

Supposed to be a neg there... Then IBP?

20. idku

you can also say, $\Large \int\limits_{ }^{ }te^{-3t}dt$ $\Large \frac{1}{-9}\int\limits_{ }^{ }-3(-3t)e^{-3t}dt$ (i used a magic 1) $u=-3t~~~du=-3dt$ $\Large \frac{1}{-9}\int\limits_{ }^{ }\color{blue}{-3}\color{red}{(-3t)}e^{\color{red}{-3t}}\color{blue}{dt}$

21. idku

the blue part is the part that gets replaced by du. the red - each thing is a u

22. AmTran_Bus

Where is the 1/9 from? I would like to do it the way I have just started.

23. idku

oh, 1/9 not 1/-9

24. AmTran_Bus

|dw:1434926879794:dw|

25. idku

i multiply times -3 times -3 and times 1/9

26. idku

and write that all out, to have my u's

27. idku

u don't have to do it like this. I am preparing my integral for the sub. U also can do the sub and rearrange then.

28. idku

$\Large \frac{1}{9}\int\limits\limits_{ }^{ }-3(-3t)e^{-3t}dt$ (the only thing is like this) no -9 on bottom, it is positive

29. idku

bye

30. anonymous

Refer to the attachment from WolframAlpha.

31. AmTran_Bus

Thanks...but I really want to work it from scratch on my own.

32. AmTran_Bus

|dw:1434927052945:dw|

33. AmTran_Bus

If it were me, I'd do IBP first.|dw:1434927094434:dw|

34. AmTran_Bus

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35. AmTran_Bus

At this point, what do I do?

36. AmTran_Bus

Well, this is no help. Closed.

37. Zale101

$\Large \int\limits_{}^{}te^{-3t}dt$ u=t and du=dt dv=e^(-3t) and v=(-1/3)e^(-3t) Now, use IBP $$uv-\int\limits_{}^{}vdu$$ $$\large =-\frac{1}{3}te^{-3t}-\int\limits_{}^{}(-\frac{1}{3})e^{-3t}dt$$ $$\large =-\frac{1}{3}te^{-3t}+\frac{1}{3}\int\limits_{}^{}e^{-3t}dt=-\frac{1}{3}te^{-3t}-\frac{1}{9}e^{-3t}+c$$