Register to reply 
Indefinite integral problem 
Share this thread: 
#1
Nov1012, 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) 


#2
Nov1012, 03:00 AM

Emeritus
Sci Advisor
HW Helper
Thanks
PF Gold
P: 11,747

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?



#3
Nov1012, 07:38 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,533

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]? 


#4
Nov1212, 05:51 AM

P: 4

Indefinite integral problem
no i do not. can you tell me please?



#5
Nov1212, 06:06 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,533

This isn't for a class? Do you know the derivative of e^{ax}?



#6
Nov1212, 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.



#7
Nov1212, 11:50 PM

Emeritus
Sci Advisor
HW Helper
PF Gold
P: 7,808

If so, use it ti find the derivative of e^{ax}, 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 