Register to reply

Indefinite integral problem

by gyza502
Tags: e^x, help a noob, indefinite integral
Share this thread:
gyza502
#1
Nov10-12, 02:45 AM
P: 4
1. The problem statement, all variables and given/known data
F(x)= (3^x)(e^x)dx



2. Relevant equations
F(u)=U^n=(U^(n+1))/n+1


3. The attempt at a solution
I said it equaled:
((3^(x+1))/(x+1))(e^x)
Phys.Org News Partner Science news on Phys.org
Law changed to allow 'unlocking' cellphones
Microsoft sues Samsung alleging contract breach
Best evidence yet for coronal heating theory detected by NASA sounding rocket
vela
#2
Nov10-12, 03:00 AM
Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,692
Your post doesn't make sense. Why don't you write things out using normal notation so we don't have to guess as to what you mean?
HallsofIvy
#3
Nov10-12, 07:38 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363
You've made a number of very basic errors. First, and this may be what Vela was complaining about, it doesn't make sense to have a function equal to an integrand- what you meant to say, instead of [itex]F(x)= 3^xe^xdx[/itex] was that the integrand was [itex]3^x e^x dx[/itex] or, equivalently that you were trying to find [itex]F(x)= \int 3^xe^x dx[/itex].

You make the same kind of error when you write "F(u)=U^n=(U^(n+1))/n+1". [itex]U^{n+1}/(n+1)[/itex] is the integral of [itex]U^n[/itex], they are not equal. (Oh, and two minor things- "u" and "U" are not interchangeable and what you wrote, U^(n+1)/n+ 1 is equal to (U^(n+1)/n)+ 1, not U^(n+1)/(n+1).)

Most importantly, that "power rule" does not apply here. It applies to the variable to a constant power and what you have here is a constant to a variable power. And, of course, you cannot simply multiply by [itex]e^x[/itex] as if it were a constant.

Instead, use the fact that [itex]3^x= e^{ln 3^x}= e^{xln(3)}[/itex] and write the integral, [itex]\int 3^xe^x dx[/itex], as [itex]\int e^{x ln(3)}e^x dx= \int e^{x ln(3)+ x}dx= \int e^{x(ln(3)+ 1)}dx[/itex].

Now, do you know how to integrate [itex]\int e^{ax}dx[/itex]?

gyza502
#4
Nov12-12, 05:51 AM
P: 4
Indefinite integral problem

no i do not. can you tell me please?
HallsofIvy
#5
Nov12-12, 06:06 AM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,363
This isn't for a class? Do you know the derivative of eax?
gyza502
#6
Nov12-12, 10:18 PM
P: 4
yes it is for a class. But, it is a practice problem. We haven't seen similar problems to this, so i am quite lost at the moment. I know the derivative of e^x is e^x.
SammyS
#7
Nov12-12, 11:50 PM
Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,801
Quote Quote by gyza502 View Post
yes it is for a class. But, it is a practice problem. We haven't seen similar problems to this, so i am quite lost at the moment. I know the derivative of e^x is e^x.
Do you know the chain rule ?

If so, use it ti find the derivative of eax, a being a constant.


Register to reply

Related Discussions
Difficult Indefinite Integral (substitution problem?) Calculus & Beyond Homework 9
Indefinite Integral Problem Calculus & Beyond Homework 8
Indefinite integral help Calculus 2
Indefinite integral problem Calculus 6
Indefinite integral Calculus & Beyond Homework 1