# Math Help - Integration

1. ## Integration

hi, i have to integrate the following expression:

3e^-.8t multiplied by sin(t)

i'm a little confused as to how to go about this, so if anyone could help i'd appreciate it!

2. i think you can use u-substitution to solve this problem.

just make -.8t=u

then du=-.8dt

so, dt= (-1/.8)du, or, dt= (-10/8)du

hopefully this helps and is not wrong...

3. Originally Posted by clockingly
hi, i have to integrate the following expression:

3e^-.8t multiplied by sin(t)

i'm a little confused as to how to go about this, so if anyone could help i'd appreciate it!
The derivation is long the standard way. It is simpler with complex analysis but I assume you do not know that method. Thus, instead of deriving it I will just mention a formula,

For $a,b\not = 0$.
$\int e^{ax}\sin bx dx = \frac{e^{ax}}{a^2+b^2}(a\sin bx - b\cos bx)+C$

4. Thanks!

But what do you do if there is a constant in front of the e (there is a 3 in front)?

5. Originally Posted by clockingly
Thanks!

But what do you do if there is a constant in front of the e (there is a 3 in front)?
Rememeber any constant function can always be factored out of the integrand. Thus, you can do the problem without the 3, and when you finish multiply everything by 3.

6. OHHHH!! That helped a lot! Thanks!