- #1
nusaibahazman
- 6
- 0
1. how to integrate∫ (ln x)2 /x dx
nusaibahazman said:1. how to integrate∫ (ln x)2 /x dx
raopeng said:Here it is better to show what you have attempted so far, after all people here are not answer machine. But a hint can be: what is the derivative of ln x?
The derivative of ln(x) is (1/x) + C .nusaibahazman said:x(ln x)-1+c..i not pretty sure..
After doing all that, what does your integral become, in terms of u ?nusaibahazman said:i know..let u= ln x
then differenciate du/dx= 1/x..
The integration of the natural log, also known as the integral of ln(x), is a mathematical operation that finds the function whose derivative is equal to the natural log function. It is denoted by ∫ln(x) dx.
Integration of the natural log is important in many mathematical and scientific applications. It is used to solve differential equations, calculate areas under curves, and model various natural phenomena, such as population growth and radioactive decay.
The natural log function can be integrated using the integration by parts method, where the natural log function is broken down into two parts and integrated separately. The resulting integral can then be solved using substitution or other integration techniques.
Yes, there are a few special rules for integrating the natural log function. For example, the integral of ln(1) is equal to 0 and the integral of ln(x) divided by x is equal to ln(x) squared plus a constant. These rules can be helpful in certain integration problems.
Yes, most mathematical software, such as Mathematica and MATLAB, have built-in functions for integrating the natural log. These programs use sophisticated algorithms to find the exact or approximate solution to the integral. However, it is important to understand the concepts and techniques behind integration before relying solely on software.