Introduction
Integration is a core part of calculus, often presenting unique challenges that require creative ways to solve. In this post, I will share some of the interesting integration problems I have encountered, along with their solutions. Take some time to try them out before checking out my solutions!
Problem 1
Evaluate the integral within 30 seconds:
\[
\int x^\frac{1}{\ln(x)} \, dx
\]
Solution:
$$ \begin{aligned} u &= x^{\frac{1}{\ln(x)}} \\ &= e^{\ln(x) \times \frac{1}{\ln(x)}} \\ &= e \\ \int e \, dx &= ex + C \end{aligned} $$