Math Is Fun Forum

lijon

Member

Registered: 2010-02-11

Posts: 4

Integration problems

There are 3 problems that I'm stuck with and have no idea where to begin:

1)
Integrate 2x(1-sin2x) dx

2)
Integrate ((3x^2)+1)/x^2((x^2)+1)^2 dx

3)
Integrate x cos x (e^x) dx

I'm thinking that 1 has something to do with substitution and 2 has to do with partial fraction? 3 should be integrate by parts. From then on I'm totally lost...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Integration problems

Hi;

For 2)

If this is the problem:

One way would be to split it into partial fractions:

Now integrate term by term.

---

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.

lijon

Member

Registered: 2010-02-11

Posts: 4

Re: Integration problems

Hi;

For 2)

If this is the problem:

One way would be to split it into partial fractions:

Now integrate term by term.

Thanks for the reply, I'm just wondering how did you get from

to

?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Integration problems

Hi lijon;

This is a really nice page and I use it myself;

http://en.wikipedia.org/wiki/Partial_fraction

Since the denominator is already factored for you.
This one is a repeated factor in the denominator. Your denominators will be of the form:

Can you work it now, if not, I will show you my method.

---

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.