Question

What is the antiderivative of `(5x)/(x^2+1)`?

Answer 1

`F(x) = 5/2ln(x^2+1)+C`

Explanation:

The primitive of a function can be calculated as its indefinite integral:

`F(x) = int (5x)/(x^2+1)dx`

This integral can be calculated easily noting that:

`d(x^2+1) = 2xdx` so:

`int (5x)/(x^2+1)dx = 5/2 int (2xdx)/(x^2+1) = 5/2 int (d(x^2+1))/(x^2+1)= 5/2ln(x^2+1)+C`