Final answer:
U-substitution, also known as the chain rule, is a technique used in calculus to simplify integrals. The steps of u-substitution involve identifying 'u', calculating its derivative, and replacing parts of the integral to make it simpler. By using u-substitution, complicated integrals can be transformed into simpler ones.
Step-by-step explanation:
U-substitution, also known as the chain rule, is a technique used in calculus to simplify integrals. The steps of u-substitution are as follows:
- Identify a part of the integral as 'u'.
- Calculate the derivative of 'u' with respect to 'x'.
- Replace that part of the integral with 'u' and replace 'dx' with 'du'.
- Integrate the new expression, which should now be simpler.
- Replace 'u' and 'du' with the original variable and differential, if needed.
By using u-substitution, we can transform complicated integrals into simpler ones, making them easier to solve.