Integration by substitution is a method used in calculus to find the integral of a function by substituting a variable with a new one. This technique is also known as the "chain rule" or "u-substitution."
To use integration by substitution for (1+x)/(1-x), we first substitute the variable (1-x) with a new variable u. Then, we find the derivative of u (du) and substitute it into the equation. This will give us an integral with only one variable, which we can then solve using basic integration techniques.
Integration by substitution is useful for (1+x)/(1-x) because it simplifies the integral and makes it easier to solve. By substituting a new variable, we can reduce the complexity of the integral and solve it using basic integration rules.
The steps for integrating (1+x)/(1-x) using substitution are as follows:
1. Substitute the variable (1-x) with a new variable u.
2. Find the derivative of u (du) and substitute it into the equation.
3. Simplify the integral by substituting (1-x) with u.
4. Integrate the new equation using basic integration rules.
5. Substitute back the original variable (1-x) with u to get the final solution.
Yes, integration by substitution can be used for any function. However, it is most effective for functions that are difficult to integrate using basic rules. It is a useful technique to simplify the integral and make it easier to solve.