# Integral error

1. Feb 12, 2014

1. The problem statement, all variables and given/known data

Evaluate: $$\int{xe^{ax}}dx$$

2. Relevant equations

Integration by substitution

3. The attempt at a solution

I'm on a phone at the moment. My work: http://postimg.org/image/v4hdr5uqx/ [Broken]

$$\frac{xe^{ax}}{a}-\frac{e^{ax}}{a^2}$$

Last edited by a moderator: May 6, 2017
2. Feb 12, 2014

### SteamKing

Staff Emeritus
You should do this integral by parts. Some of your original substitutions don't look OK.

3. Feb 12, 2014

http://postimg.org/image/ao3mi4ygz/ [Broken]

I feel like I'm getting closer but I'm still making a dumb mistake. Is it with the derivatives?

Last edited by a moderator: May 6, 2017
4. Feb 12, 2014

### eumyang

If $dv = e^{ax} dx$, then $v = e^{ax}$ is wrong. There are also multiple errors on the second line, but you need to fix what I said first.

5. Feb 13, 2014

$$\int{xe^{ax}}dx$$ $$u=x du=dx dv=e^{ax}dx v=\frac{e^{ax}}{a}$$
$$\frac{xe^{ax}}{a}-\int{\frac{e^{ax}}{a}}dx$$
$$\frac{xe^{ax}}{a}-\int{e^{ax}a^{-1}}dx=\frac{xe^{ax}}{a}-\frac{e^{ax}}{a^2}$$