Integration by Substitution is a valuable technique for solving integrals that involve a variable raised to a power or a trigonometric function. By replacing the variable or function with a new variable or expression, the integral can be simplified into a form that is easier to integrate.
While substitution can be an effective method for solving difficult integrals, it may not always be the simplest or most straightforward approach. Other techniques, such as partial fractions, long division, and trigonometric identities, may be more appropriate for certain integrals.
In general, it is essential to have a variety of integration techniques at your disposal and to choose the method that best fits the specific integral you are trying to solve. Practice and experience can help you develop a better sense of which techniques to use in different situations.
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