- #1

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## Homework Statement

1.)

[tex]\int{\frac{t}{(1+t^{2})^3}dt}[/tex]

2.)

[tex]\int{xe^{-2x}dx.}[/tex]

3.)

[tex]\int{\frac{x.dx}{2+x^{2}}}[/tex]

This one is inegrating between 2 and 0, but I didn't know how to format that in.

4.)

[tex]\int{\frac{cos t}{1 + sin t}dt.}[/tex]

## Homework Equations

Q 1.)

I'm substituting [tex]u = 1 + t^{2}[/tex]

Q 2.)

[tex] uv - \int{vdu}[/tex]

where u = x

and

dv = [tex]e^{-2x}[/tex]

Q 3 & 4.)

I'm afraid I'm well and truly stuck with these, I think for number 3 I want to use function over a function rule possibly?

## The Attempt at a Solution

Promise not to laugh ok

1.)

Rearranging to [tex]\int{t.u^{-3}}[/tex]

using [tex] uv - \int{vdu}[/tex]

[tex] t.\frac{-1}{2}u^{-2} - \int{\frac{-1}{2}u^{-2}.t^{2}[/tex]

which is:

[tex] t.\frac{-1}{2}u^{-2} - (u^{-2}.\frac{1}{3}t^{3})[/tex]

Am I anywhere close?

As for the others I'm afraid I've not much idea.

2.) could be

using [tex] uv - \int{vdu}[/tex] again:

[tex]x.-2e^{-2x} - \int{-2e^{-2x}}[/tex]

which goes to

[tex]x.-2e^{-2x} - 4e^{-2x}[/tex]

But once again, I could be wildly wrong.

**It's not so much that I think I'm going wrong, it's more that I've no idea how to approach the questions. Any nudges in the right direction would be fantastic**

Thank you.