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When the integrand is formed by a product (or a division, which we can treat like a product) it's recommended the use of the method known as integration by u-substitution, that consists in applying the following formula:
Even though it's a simple formula, it has to be applied correctly. Let's see a few tips on how to apply it well:
Example 1
Notes: it doesn't matter if cos(x) in u or dv (due to the fact we obtain a sinus). We choose u = x to reduce it's degree (and that way x disappears). If we choose dv = x, we increase the degree.
Example 2
In this integral we don't have an explicit product of functions, but we don't know what the logarithms primitive function is, so we differentiate it, that way u = ln(x).
Example 3
It's in our interest to select u = x2 (to reduce the exponent) but then we're forced that dv = ln(x) and obtaining v isn't immediate. So we'll select the other case
More examples: Integration by U-substitution: resolved integrals step by step
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Fecha publicación: 6.2.2017
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