# Indefinite integral problem

1. Nov 10, 2012

### gyza502

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. Nov 10, 2012

### vela

Staff Emeritus
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. Nov 10, 2012

### HallsofIvy

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 $F(x)= 3^xe^xdx$ was that the integrand was $3^x e^x dx$ or, equivalently that you were trying to find $F(x)= \int 3^xe^x dx$.

You make the same kind of error when you write "F(u)=U^n=(U^(n+1))/n+1". $U^{n+1}/(n+1)$ is the integral of $U^n$, 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 $e^x$ as if it were a constant.

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

Now, do you know how to integrate $\int e^{ax}dx$?

4. Nov 12, 2012

### gyza502

no i do not. can you tell me please?

5. Nov 12, 2012

### HallsofIvy

This isn't for a class? Do you know the derivative of eax?

6. Nov 12, 2012

### gyza502

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. Nov 12, 2012

### SammyS

Staff Emeritus
Do you know the chain rule ?

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

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