# How do you know When to use integration by substitution?

I would try Integration by Substitution if an integrand is a composition of functions.

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Integration by substitution, also known as u-substitution, is a technique used to simplify integrals by replacing variables. It is particularly useful when the integrand contains a composite function or a function and its derivative. You should use integration by substitution when you encounter integrals where a straightforward method, such as power rule or trigonometric identities, is not applicable, but a change of variables can simplify the integral. The key is to identify a suitable substitution that will make the integral more manageable, typically by letting u be a function or part of the integrand's expression and then finding du to replace dx. This technique can help transform complex integrals into simpler forms, making them easier to evaluate.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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