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

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Answer 1 · 2017-01-10T23:28:06

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

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:

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

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