Integral of lnx/x^2

TL;DR

Learn how to integrate ln(x) / x^2 using integration by parts.

Transcript

in this video we're going to focus on finding the indefinite integral of the natural log of x divided by x squared dx so how can we integrate that function we need to use something called integration by parts the integral of u dv is equal to u times v minus the integral of v d u so i'm going to rewrite the integral like this it's going to be ln x t... Read More

Key Insights

• 🥳 Integration by parts is a helpful technique for integrating products of functions.
• 🛫 Identifying u and dv correctly is crucial for using the integration by parts formula.
• 🥳 The integral of ln(x) can be challenging to compute without integration by parts.
• ✊ The power rule for integration is useful for integrating functions in the form of x^n.

Summary & Key Takeaways

• Integration by parts is used to find the indefinite integral of ln(x) / x^2.

• Letting u = ln(x), the derivative du is 1/x dx, and the integral of dv = 1/x^2 dx is -1/x.

• Applying the integration by parts formula, the final answer is -ln(x)/x - 1/x + C.