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Hello, Forum!

I just registered after seeing you actually help people understand their problems. That's great.

We have (or should have) learned about linearity, substitution and partial integration. However, I don't know when to use which! Could someone also give me a bit of an expanation on this? :(

I have to solve an integral:

x*e^(-3x) dx

My train of thought: I have almost got 2 'basis integrals': x dx and e^x dx. I probably need to substitute to get them to the basic form. But how!

As you see I'm pretty clueless, but what I came up with was:

u = -3x --> u'= -3

v' = x --> v = (x²)/2

However, this leads nowhere. I don't know what to do!

According to derive, the solution is supposed to be:

I sincerely hope someone will be able to show me the light!

Thanks in advance.

PS: Our teacher is really bad at teaching!

I just registered after seeing you actually help people understand their problems. That's great.

We have (or should have) learned about linearity, substitution and partial integration. However, I don't know when to use which! Could someone also give me a bit of an expanation on this? :(

I have to solve an integral:

x*e^(-3x) dx

My train of thought: I have almost got 2 'basis integrals': x dx and e^x dx. I probably need to substitute to get them to the basic form. But how!

As you see I'm pretty clueless, but what I came up with was:

u = -3x --> u'= -3

v' = x --> v = (x²)/2

However, this leads nowhere. I don't know what to do!

According to derive, the solution is supposed to be:

Code:

```
1 -3x ⎛ x 1 ⎞
⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯ - e ⎜⎯⎯⎯⎯⎯⎯⎯⎯⎯ + ⎯⎯⎯⎯⎯⎯ ⎟
2 ⎜ 3·LN(e) 2⎟
9·LN(e) ⎝ 9·LN(e) ⎠
```

Thanks in advance.

PS: Our teacher is really bad at teaching!

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