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Finding the indefinite integral of cos (5x)/e^ [sin (5x)]. To do that, we need to perform 𝘶-substitution twice.

How do you do u substitution right over here? And the key when you have powers of trig functions, especially when you have one of them as an odd power, what you want to do is …

Before diving into our practice exercise, gain some risk-free experience performing 𝘶-substitution. Find each indefinite integral.

𝘶-substitution: indefinite integrals Google Classroom Microsoft Teams ∫ 3 x 2 (x 3 + 1) 6 d x =

Well we just said u is equal to sine of x, you reverse substitute, and you're going to get exactly that right over here. So when we talk about the reverse chain rule, it's essentially just doing u …

Using 𝘶-substitution in a situation that is a bit different than "classic" 𝘶-substitution. In this case, the substitution helps us take a hairy expression and make it easier to expand and integrate.

In the u-substitution exercises for definite integrals, the next exercise asks us to integrate functions like 1/ (1+x²) and check our answer using the derivative of arctan (x), even though …

Given an integral that should be found using u-substitution, determine what u should be.

Key takeaway: Sometimes we need to multiply or divide the entire integral by a constant, so we can achieve the appropriate form for u -substitution without changing the value of the integral.