# Homework Help: Simple Indefinite Integral

1. May 28, 2010

### Procrastinate

$$\int\frac{4}{-e^{4x-7}}$$

$$=ln-e^{4x-7}}$$

$$=-4x+7+C$$

$$=\-e^{-4x+7}+C$$

Last edited: May 28, 2010
2. May 28, 2010

### D H

Staff Emeritus
The book is right, which is easily verifiable by computing the derivative the given answer.

3. May 28, 2010

### Procrastinate

Is there somewhere I went wrong? I am guessing it has something to do with the ln.
I thought that

$$\ln{e}=1$$

Therefore: $$ln-e^{4x-7}}=-4x+7+C$$

Last edited: May 28, 2010
4. May 28, 2010

### D H

Staff Emeritus
Yes, the problem is with the natural logarithm.

Just because $\int \frac 1 x \,dx = \ln x$ does not mean that everything of the form $\int \frac 1{f(x)}\,dx$ integrates to $\ln(f(x))$.