At its basic form, substitution is used when an integral contains some function and its derivative. It is the reverse chain rule (click here for a quick review).

The substation rule is as follows:

Let’s see how it works, starting with the logarithmic function (click here):

Here’s an example of exponential functions (click here):

Here’s an example using the power rule (click here):

Here’s an example using simple trig substitution (click here):

Sometimes the appropriate substitution is not that obvious and requires some extra work. We’ll walk you through more advanced examples in the next post

Cheers,

Michal

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More examples of integration by parts.

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