### May 11, 2004

I removed the links on all the code examples. There's really no need for them.

And now, for a pretty cool math task I did today.

Find the indefinite integral of the following function:

$$f(x) = ae^x - \frac{1}{2b\sqrt{x}}$$

We start by setting it up:

$$\int{\left(ae^x - \frac{1}{2b\sqrt{x}}\right)} dx$$

I'll turn the expressions into exponentials, so that we can integrate them:

$$\int{\left(ae^x - \frac{1}{2} b^{-1} x^{-\frac{1}{2}}\right)} dx = ae^x - b^{-1}\sqrt{x} + C$$

This gives us the following integrated function:

$$F(x) = ae^x - \frac{\sqrt{x}}{b} + C$$