Problems on integration by partial fractions Problem no 14 - Integration - Diploma Maths - 2

TL;DR

This video demonstrates how to convert a rational form into partial form using integration by partial fractions.

Transcript

click the bell icon to get latest videos from Ekeed Hello friends in this video we are going to continue one more problem on integration by partial fractions let us start with problem number 14 integral X square plus X plus 3 upon X plus 2 into X square plus 1 DX here you can see one part is already factorized by the other part cannot be factorized... Read More

Key Insights

• 😑 Integration by partial fractions is a useful technique for solving rational expressions.
• 😑 Factorizing one part of the expression and expressing the other part as fractions allows for easier integration.
• ☺️ Specific values of x can be substituted into the equation to solve for the unknown constants.

Questions & Answers

Q: What is the objective of the video?

The video aims to explain how to convert a rational form into partial form using integration by partial fractions.

Q: How is the problem in the video solved?

The problem involves factorizing one part of the rational expression and expressing the other part as fractions. Then, integration is performed to obtain the solution.

Q: How are the values of a, b, and c determined?

The values of a, b, and c are determined by substituting specific values of x into the equation and solving for the unknowns.

Q: What is the final answer to the integration problem?

The final answer is given as log(X + 2) + arctan(X) + C, where C is the constant of integration.

Summary & Key Takeaways

• The video explains the process of converting a rational form into partial form using integration by partial fractions through a specific example.

• The problem involves integrating (X^2 + X + 3) / (X + 2)(X^2 + 1).

• By factorizing one part and expressing the other part as fractions, the solution is obtained through integration.