- #1
iNCREDiBLE
- 128
- 0
How do I integrate:
[tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex]
[tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex]
Tom Mattson said:You have to show us how you started first.
Partial integration is a method used in calculus to find the integral of a function by breaking it down into simpler parts and integrating each part separately. It is useful when the integrand is a product of two functions, one of which is easier to integrate than the other.
In the case of [tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex], we can use the formula for partial integration, which is [tex]\int u dv = uv - \int v du[/itex], where u and v are two functions. In this case, we can let u = arctan(x) and dv = [tex]\frac{x}{(1+x^2)^2}[/itex].
There is no specific rule for choosing the values of u and dv for partial integration. However, in most cases, it is helpful to choose u as the more complicated function and dv as the simpler function.
The steps for solving [tex]\frac{xarctan(x)}{(1+x^2)^2}[/itex] using partial integration are:
Some common mistakes to avoid when using partial integration are: