# Integral of x*cos(5x) with DI method | Summary and Q&A

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February 7, 2015
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blackpenredpen
Integral of x*cos(5x) with DI method

## TL;DR

Learn a faster method for integration by parts called the DI Method.

## Key Insights

• 🥳 The DI Method is a simplified technique for integration by parts, making it faster and easier to solve certain integrals.
• 🪡 By focusing on what needs to be differentiated and integrated, the DI Method eliminates the need for complex notation and calculations.
• 😫 The DI Method involves setting up a table with columns for D and I, allowing for a clear organization of the integration process.
• ❓ By choosing the appropriate functions for differentiation and integration, the DI Method eliminates unnecessary steps and simplifies the solution.
• 🤝 The DI Method can be a useful tool in mathematics, particularly when dealing with integrals that involve products of functions.
• 🙈 The key to using the DI Method effectively is to recognize when to stop differentiating or integrating based on the presence of zeros in the D column.
• 🤘 The resulting solution using the DI Method involves multiplying diagonally and accounting for the signs, providing a concise answer.

## Transcript

let me show you a much faster way to do the integral of x * cosine of 5x we still have to do integration by parts and then the traditional formula for integration proporties the integral of U DV is equal to UV minus the integral of v duu and what this is saying is that look at our integral and we have to pick something for U and we have to differen... Read More

### Q: What is the DI Method for integration by parts?

The DI Method simplifies integration by parts by focusing on what needs to be differentiated (D) and integrated (I), streamlining the process for faster solutions.

### Q: How does the DI Method work?

The DI Method involves setting up a table with columns for D and I, and alternating signs. By choosing the functions to differentiate and integrate, you can simplify the integration process.

### Q: How is the integral of x * cosine of 5x solved using the DI Method?

By choosing cosine of 5x to integrate and x to differentiate, the DI Method simplifies the steps. The resulting solution involves multiplying diagonally and accounting for the signs, resulting in a faster solution.

### Q: Are there any limitations to using the DI Method?

The DI Method is a technique to simplify integration by parts, but it may not be applicable to all types of integrals. Complex functions or specific cases may require different approaches.

## Summary & Key Takeaways

• The DI Method is a faster way of doing integration by parts, simplifying the process.

• By focusing on what needs to be differentiated and what needs to be integrated, the DI Method streamlines the steps.

• In the provided example, the DI Method is used to solve the integral of x * cosine of 5x, resulting in a simplified and quicker solution.