Question

How to find the indefinite integral of (e^-t)(1+3sin(t))dt?

Answer 1

You can't.

Answer 2

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

Answer 3

True, true.

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

http://5z8.info/fakelogin_v3z6yt_begin-bank-account-xfer

Answer 9

What is your link suppose to be, Realist?

Answer 10

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

Answer 11

It's supposed to be opened. @GoldPhenoix

Answer 12

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

Answer 13

Thanks a lot.

Answer 14

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

Answer 15

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

Answer 16

can I know where does that table come from?

Answer 17

Ummm its on the back page of every calc book

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

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