Respuesta :
Using integration by parts, the application of integration by parts corresponds to applying the product rule to the product of functions u(x) = ln(x) and v(x) = (x^13)/13.
What is the integration by parts?
Integration by parts is similar to the inverse of the product rule, and is given as follows:
[tex]\int u dv = uv - \int v du[/tex]
Hence it is the product of functions u and dv. To identify function u, the precedence is given is as follows:
- L: Logarithmic.
- I: Inverse.
- A: Arithmetic.
- T: Trigonometric.
- E: Exponential.
In this problem, we have a logarithmic and an arithmetic function, hence:
- Function u is the logarithmic function ln(x).
- Function g is ∫x^12 dx, hence x^13/13.
The application of integration by parts corresponds to applying the product rule to the product of functions u(x) = ln(x) and v(x) = (x^13)/13.
More can be learned about integration by parts at https://brainly.com/question/24171063
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