U-Substitution is a technique used in integration to simplify a given expression by replacing a complicated expression with a simpler one. In the case of (x-5)/√(x-6), u-Substitution is used to replace the variable x with a simpler expression u, making the integration process easier.
The u-value is usually chosen to be the inner function of a composite function. In this case, the expression (x-5) is inside the square root function, so we let u = x-5.
The general process for integrating using u-Substitution is as follows:
No, u-Substitution is a powerful technique, but it can only be used for certain types of integrals. It is most commonly used for integrals involving composite functions, such as (x-5)/√(x-6).
Yes, there are other techniques such as integration by parts, trigonometric substitutions, and partial fractions. However, u-Substitution is the most efficient method for integrating (x-5)/√(x-6) as it simplifies the expression and makes the integration process easier.