1. ## Integral of (4t-2)*e^(t^2-t).

I wish to integrate (4t-2)*e^(t^2-t).

U=4t-2
du/dt = 4

dv=e^(t^2-t)
dv/dt = ?

Am I even on the right track?

2. ## Re: Integral of (4t-2)*e^(t^2-t).

We have:
$\displaystyle \int (4t-2)e^{t^2-t}dt$
which we can write as:
$\displaystyle 2\int (2t-1)e^{t^2-t}dt$

Now, let $\displaystyle t^2-t=u$

(Do you see why this is a good substitution?)

3. ## Re: Integral of (4t-2)*e^(t^2-t).

What is the derivative of $\displaystyle t^{2}-t$?... is it somewhere in the integrand function?...

Marry Christmas from Serbia

$\displaystyle \chi$ $\displaystyle \sigma$

4. ## Re: Integral of (4t-2)*e^(t^2-t).

int t^2-t = 2t-1

Do I then use Integration by parts with dv = ?

5. ## Re: Integral of (4t-2)*e^(t^2-t).

No, you don't need integration by parts. Have you done substitutions (in integration) before?
Let $\displaystyle t^2-t=u \Rightarrow (2t-1)dt=du$

Do you see how you can use this?

6. ## Re: Integral of (4t-2)*e^(t^2-t).

Thank you people - got it - U substitution.

2 int (2t-1)*e^(t^2-t) dt
= 2 int e^u du
= 2*e^u + c
= 2*e^(t^2-t) + c

7. ## Re: Integral of (4t-2)*e^(t^2-t).

Yes, that's correct.