Primitive of a definite integral

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To find the function F(x), the integral of F(x) from 0 to r is given as equal to (r^3)/((r^2+A)^(3/2)) + N, where A and N are constants. The discussion emphasizes the relationship between differentiation and integration, suggesting that taking the derivative of the right-hand side (RHS) can help identify F(x). The user attempted to solve the problem by evaluating the derivative but is uncertain about the next steps. Clarification is sought on how the derivative of the RHS relates to F(x). Understanding this relationship is crucial for solving the integral equation.
PeteSampras
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Homework Statement


I need find the function ##F(x)## .

Homework Equations


##\int_0^r F(x)dx = \frac{r^3}{(r^2+A)^{3/2}}+N##

where ##A,N## are constants.

The Attempt at a Solution


I tried using some function of test, for instance the derivative of the right function evaluated in x. But , i don't know how to solve this problem.
 
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Hi Pete:

What is the relationship between a differential and an integral? What did you get as the derivative of RHS? How does this relate to F(x)?

Hope this helps?

Regards,
Buzz
 

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