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u-substitution

9 videos
1 skill
U-substitution is a must-have tool for any integrating arsenal (tools aren't normally put in arsenals, but that sounds better than toolkit). It is essentially the reverise chain rule. U-substitution is very useful for any integral where an expression is of the form g(f(x))f'(x)(and a few other cases). Over time, you'll be able to do these in your head without necessarily even explicitly substituting. Why the letter "u"? Well, it could have been anything, but this is the convention. I guess why not the letter "u" :)

u-substitution

VIDEO 5:11 minutes
Using u-substitution to find the anti-derivative of a function. Seeing that u-substitution is the inverse of the chain rule.

u-substitution example 2

VIDEO 4:04 minutes
Another example of using u-subsitution

u-substitution example 3

VIDEO 5:33 minutes
Manipulating the expression to make u-substitution a little more obvious.

u-substitution with ln(x)

VIDEO 3:39 minutes
Doing u-substitution with ln(x)

(2^(ln x))/x antiderivative example

VIDEO 8:40 minutes
Finding  ∫(2^ln x)/x dx

u-substitution and back substitution

VIDEO 5:01 minutes
Using u-substitution and "back substituting" for x to simplify an expression

u-substitution with definite integral

VIDEO 5:39 minutes
Example of using u-substitution to evaluate a definite integral

Doing u-substitution twice (second time with w)

VIDEO 8:57 minutes
Example where we do substitution twice to get the integral into a reasonable form