Question

How do you find the antiderivative of `1/((x^2+25)^2) dx`?

Answer 1

`dy/dx =( -4x)/(x^2+25)^(-3)`

Explanation:

In order to have a simple solution, the above expression can be written as

`y = (x^2+25)^(-2)`

Now use function of a function rule

`dy/dx = -2(x^2+25)^(-3)(2x)`
`dy/dx = -4x(x^2+25)^(-3)`
`dy/dx =( -4x)/(x^2+25)^(-3)`

You can use the quotient rule also