# Homework Help: What trick is used to integrate this?

1. Jul 20, 2011

### flyingpig

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

$$\int e^x \frac{1 + sin(x)}{1 + cos(x)}\;dx$$

3. The attempt at a solution

Apparently there is a trick involving e^x integrals like this

$$\int e^x[f(x) + f'(x)] dx = e^x f(x) + C$$

Now my question is not how to compute the integral above but where did this $$\int e^x[f(x) + f'(x)] dx = e^x f(x) + C$$ identity came from?? How does one know this exists?

2. Jul 20, 2011

### SammyS

Staff Emeritus
Take the derivative of the result. That may help you see how this works.

3. Jul 20, 2011

### JKreutz

Yeah, you get this result with integration "by parts", which is the name for using the product rule to rewrite integrals (hopefully in a form you can recognize and solve). If you take a second-semester single-variable calculus class you'll learn about this.