I didn't get the whole problem oO
But the antiderivate of is easy to find.
An antiderivative of is
As you've calculated, an antiderivative will be
What do you mean by proportional ? You have a function equal to :
with a a constant ?
If so, it's ok, the antiderivative doesn't take care of the constants...
An antiderivative of f will be a*[antiderivative of 1/(10+x)^2]