A community for students.
Here's the question you clicked on:
 0 viewing
Idealist
 2 years ago
How to find the indefinite integral of (e^t)(1+3sin(t))dt?
Idealist
 2 years ago
How to find the indefinite integral of (e^t)(1+3sin(t))dt?

This Question is Closed

Idealist
 2 years ago
Best ResponseYou've already chosen the best response.0Yes, you could. There's an answer for this.

Realist
 2 years ago
Best ResponseYou've already chosen the best response.1integral 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.

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3Well lets separate it to \( \int e^{t}dt +3\int e^{t}sin(t)dt\)

Realist
 2 years ago
Best ResponseYou've already chosen the best response.1Credit: A beautiful cheating site that works for everyone http://answers.yahoo.com/question/index?qid=20091127013306AAGvR7G

GoldPhenoix
 2 years ago
Best ResponseYou've already chosen the best response.0His question and the person who asked in answeryahoo are different. :

GoldPhenoix
 2 years ago
Best ResponseYou've already chosen the best response.0What is your link suppose to be, Realist?

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3Ok Then we get \(\large\frac{e^{t}}{t}+3(\large \frac{e^{t}}{2}(sintcost)\)

Realist
 2 years ago
Best ResponseYou've already chosen the best response.1It's supposed to be opened. @GoldPhenoix

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3Ok 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

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0@swissgirl Sorry for my dummy, I don't get the second integral.Please, explain me

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3You are not a dummy :) Umm I just used the table of integrals otherwise it gets messy

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0can I know where does that table come from?

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3Ummm its on the back page of every calc book

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3If you would like I can photocopy the page and upload it but i bet u can find it online

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0ok, 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

swissgirl
 2 years ago
Best ResponseYou've already chosen the best response.3Not necessarily is there a mistake maybe its the simplification thats the issue. It happens to me all the time

Loser66
 2 years ago
Best ResponseYou've already chosen the best response.0hey, I got it from my book too. hihi. sorry.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.