- #1
Stevieg123
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I solved this problem a couple months ago, but seem to have forgotten some rules of calculus with regards to e in the meantime. The goal is to just solve this integral. Integral from 0 to +inf of (e^tx) times (5e^-5x) dx
Now - in my work I got the answer of 5/5-t, which is correct.
In the key that I have the answer to, one tip they give is that they use the integration rule of:
Integral from 0 to +inf of e^-at dt = 1/a if a>0.So, I went at it with the standard integration by parts, but quickly realized I had forgotten some rules about multiplying e^ax X e^something else, because I couldn't terminate the integrals to get to the point of reaching 5/5-t.
Just basically did something like:
u= e^tx, dv= 5e^-5x -> du= te^tx, v=: -e^-5x
but I think I forgot a rule somewhere as when I put it into uv - S vdu form I realized I was stuck.
Does anyone know how to solve this? Do I need to do IBP a few times, or can I multiply the e's together to get to the form from before?
-or-
Do I not need to do IBP at all? Is the integral in its original form of Integral from 0 to +inf (e^tx) times (5e^-5x) dx
able to be multiplied out to get to the e^-at form required in the answer? Looking over it now, I'm starting to figure this may be true. But like I said before, I've forgotten some rules with multiplying the two together. Any help would be appreciated. Thanks.
edit - sorry for the sloppy formatting in some places, I'm unfamiliar with the codes here. I just copied the integral code from someone else's post to make it look sort of nice. The basic integral is (e^tx times 5e^-5x).
Now - in my work I got the answer of 5/5-t, which is correct.
In the key that I have the answer to, one tip they give is that they use the integration rule of:
Integral from 0 to +inf of e^-at dt = 1/a if a>0.So, I went at it with the standard integration by parts, but quickly realized I had forgotten some rules about multiplying e^ax X e^something else, because I couldn't terminate the integrals to get to the point of reaching 5/5-t.
Just basically did something like:
u= e^tx, dv= 5e^-5x -> du= te^tx, v=: -e^-5x
but I think I forgot a rule somewhere as when I put it into uv - S vdu form I realized I was stuck.
Does anyone know how to solve this? Do I need to do IBP a few times, or can I multiply the e's together to get to the form from before?
-or-
Do I not need to do IBP at all? Is the integral in its original form of Integral from 0 to +inf (e^tx) times (5e^-5x) dx
able to be multiplied out to get to the e^-at form required in the answer? Looking over it now, I'm starting to figure this may be true. But like I said before, I've forgotten some rules with multiplying the two together. Any help would be appreciated. Thanks.
edit - sorry for the sloppy formatting in some places, I'm unfamiliar with the codes here. I just copied the integral code from someone else's post to make it look sort of nice. The basic integral is (e^tx times 5e^-5x).