## Idealist Group Title How to find the indefinite integral of (e^-t)(1+3sin(t))dt? one year ago one year ago

1. Realist Group Title

You can't.

2. Idealist Group Title

Yes, you could. There's an answer for this.

3. Realist Group Title

True, true.

4. Realist Group Title

integral of e^t (1+3sin(t)) dt Expand it so e^t (1+3sin(t)) dt = (e^t + 3e^t sin(t)) dt then integrate each term and remove/factor constants so integral of e^t dt + 3 integral of e^t sin(t) dt therefore the integral of e^t dt = e^t, however for the integral: 3 integral of e^t sin(t) dt use the formula : integral of exponent ( alpha (t)) sin ( beta (t)) dt = exponent (alpha (t)) (-beta cos ((beta)(t)) + alpha sin ((beta) (t)))/ alpha^2 + beta^2 after using the formula and integrating: 3 integral of e^t sin(t) dt we get : 3/2 e^t sin(t) - 3/2e^t cos(t) then combine that with the integral of e^t dt = ? Hope you understand that. If you don't, there's absolutely nothing I can do about it.

5. swissgirl Group Title

Well lets separate it to $$\int e^{-t}dt +3\int e^{-t}sin(t)dt$$

6. Realist Group Title

Credit: A beautiful cheating site that works for everyone http://answers.yahoo.com/question/index?qid=20091127013306AAGvR7G

7. GoldPhenoix Group Title

His question and the person who asked in answeryahoo are different. :|

8. Realist Group Title
9. GoldPhenoix Group Title

10. swissgirl Group Title

Ok Then we get $$\large\frac{-e^{-t}}{t}+3(\large \frac{e^{-t}}{2}(-sint-cost)$$

11. Realist Group Title

It's supposed to be opened. @GoldPhenoix

12. swissgirl Group Title

Ok so for the first integral I used the basic rule which is $$\large \int e^{at}dt = \frac{e^{at}}{t}+C$$ And for the second integral I used $$\large \int e^{at}sinbt dt = \frac{e^{at}}{a^2+b^2}(a*sinbt- b*sinbt)+C$$ Whooopsss I forgot the +C in my answer above

13. Idealist Group Title

Thanks a lot.

14. Loser66 Group Title

@swissgirl Sorry for my dummy, I don't get the second integral.Please, explain me

15. swissgirl Group Title

You are not a dummy :) Umm I just used the table of integrals otherwise it gets messy

16. Loser66 Group Title

can I know where does that table come from?

17. swissgirl Group Title

Ummm its on the back page of every calc book

18. swissgirl Group Title

If you would like I can photocopy the page and upload it but i bet u can find it online

19. Loser66 Group Title

ok, let me check. Since I take derivative of the answer, I don't get the integrand, but a mess. hihihi... May be because I made mistake at somewhere. let me redo. Thanks for response

20. swissgirl Group Title

Not necessarily is there a mistake maybe its the simplification thats the issue. It happens to me all the time

21. Loser66 Group Title

hey, I got it from my book too. hihi. sorry.