Math Is Fun Forum

William F

Member

Registered: 2012-07-03

Posts: 16

Definite Integration with some Algebra thrown in.

I'm having trouble getting this result when I try to integrate this expression so I have a couple of questions:

1). I'm trying to use integration by parts. Am I on the right track?
2). I've been able to get the result:

and I thought there might be a way to manipulate that into the above given answer, but I'm struggling. Where am I going wrong/what is the next step?

Thanks!

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite Integration with some Algebra thrown in.

Hi William F;

Welcome to the forum.

Your answer and the first answer are not the same. Pehaps if I could see your IBP work?

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Definite Integration with some Algebra thrown in.

Yes, IBP will help you here.

Can we see your steps?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite Integration with some Algebra thrown in.

Hi William;

I am getting

for an IBP which is correct. There are other arrangements of course.

Hi anonimnystefy;

I need to eat, see you a little later.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

William F

Member

Registered: 2012-07-03

Posts: 16

Re: Definite Integration with some Algebra thrown in.

I'm not certain what you mean by IBP, so I'll show you my steps:

I'm able to get to 

From there:

Ok, so looks like on a second try I was able to match your result. I'm still not sure how it wound up as :

Some sort of factoring?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Definite Integration with some Algebra thrown in.

IBP=integration by parts.

Just factor out e^(-t).

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

William F

Member

Registered: 2012-07-03

Posts: 16

Re: Definite Integration with some Algebra thrown in.

  integration by parts of course.

Thanks! I need to review factoring apparently.

This site is great, I'll be posting here a lot in the coming months!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Definite Integration with some Algebra thrown in.

Hi

Cool! Great to have you!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Definite Integration with some Algebra thrown in.

Hi William F;

Great that you got it.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.