Integration problem

eggfriedrice

16

Integrate (t^2)e^(-3t)

I tried doing it by parts, but the answer doesn't seem to be getting me anywhere,

Reply 1

m4ths/maths247

7

Did you apply parts once.......?

Reply 2

eggfriedrice

OP

16

Original post by m4ths/maths247

Did you apply parts once.......?

I applied it again, and the equation just seems to get longer. And then it would require me to integrate a third time... and possible a fourth, I just don't see how it's going to work unless I'm doing something wrong.

Reply 3

m4ths/maths247

7

Original post by eggfriedrice

I applied it again, and the equation just seems to get longer. And then it would require me to integrate a third time... and possible a fourth, I just don't see how it's going to work unless I'm doing something wrong.

What is happening though each time you differentiate the term in t?

Reply 4

eggfriedrice

OP

16

Original post by m4ths/maths247

What is happening though each time you differentiate the term in t?

Hope you can read it.

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Reply 5

Cheesegrater4

7

make u the t^2 term maybe?

Reply 6

stephenmoffat1

Original post by eggfriedrice

Hope you can read it.

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I think you make u=t^2, and du/dx then = 2t on the first time doing parts. The once you do parts the second time round you get du/dx = 2. so then you're just integrating the exponential

Reply 7

rs232

Try the substitution u=-3t and then do the new integral by parts (several times)

Reply 8

goku24

Original post by eggfriedrice

Integrate (t^2)e^(-3t)

I tried doing it by parts, but the answer doesn't seem to be getting me anywhere,

Call it

t \cdot te^{-3t}

and then use a a mix of parts and substitution.

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Reply 9

m4ths/maths247

7

When picking u always be:

L
A
T
E

Reply 10

goku24

OP, this method is pretty useful when you have functions that are the product of a polynomial and another function:

[video="youtube;R9y-pyr-v44"]http://www.youtube.com/watch?v=R9y-pyr-v44[/video]

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Reply 11

davros

16

Original post by rs232

Try the substitution u=-3t and then do the new integral by parts (several times)

There's no need for any substitution in this question - it's just a couple of repeated integrations by parts, taking t^2 as the "first function" so that it becomes 2t and then 2 when differentiated each time.

Reply 12

eggfriedrice

OP

16

Original post by m4ths/maths247

When picking u always be:

L
A
T
E

What does LATE stand for?

Reply 13

goku24

Original post by eggfriedrice

What does LATE stand for?

Logarithms
Algebraic
Trig
Exponentials

It helps you remember what function you should make 'u' when doing IBP.

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Reply 14

rs232

Original post by davros

There's no need for any substitution in this question - it's just a couple of repeated integrations by parts, taking t^2 as the "first function" so that it becomes 2t and then 2 when differentiated each time.