find f(x) for f'(x)=3x+7

To find the function f(x) when f'(x) = 3x + 7, we need to integrate the right-hand side of the equation.

Integrating both sides, we have:

∫f'(x) dx = ∫(3x + 7) dx

Using the power rule of integration, we can integrate each term separately:

∫f'(x) dx = ∫3x dx + ∫7 dx

Integrating each term, we get:

f(x) = (3/2)x^2 + 7x + C

where C is the constant of integration.

So, the function f(x) is given by:

Answer: f(x) = (3/2)x^2 + 7x + C, where C is a constant.