📘 calculus, algebra, geometry

1. **Expand \(\frac{1}{(x-2)^7}\) to the fourth term using the binomial theorem:** The binomial theorem for negative powers states:

1. Evaluate the integral $$\int e^{e^x} \, dx$$. Let $u = e^x$, then $du = e^x \, dx$, so $dx = \frac{du}{e^x} = \frac{du}{u}$.