https://yxlow07.github.io/tags/creativity/Recent content in Creativity on Yu Xuan's PortfolioHugoen-usMon, 28 Jul 2025 12:00:00 +0800https://yxlow07.github.io/blog/integration/Thu, 15 May 2025 12:00:00 +0800https://yxlow07.github.io/blog/integration/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: $$ \begin{aligned} u &= x^{\frac{1}{\ln(x)}} \\ &= e^{\ln(x) \times \frac{1}{\ln(x)}} \\ &= e \\ \int e \, dx &= ex + C \end{aligned} $$ Problem 2 Evaluate the integral: