Clarifying integration problem

It looks like the user shared a math problem related to finding an antiderivative. They likely need to determine the constants a, b, and k such that the derivative of F(x) matches f(x) = sin(2x+3). The original antiderivative form is F(x) = -cos(ax+b)/k + C, though formatting confusion occurred while pasting the problem.

Solving the integral and finding constants

It seems the user wants the antiderivative of sin(2x+3) expressed as F(x) = -k cos(ax+b) + C, and to find the values for a, b, and k. For ∫sin(2x+3) dx, using u = 2x+3, the result is -1/2 cos(2x+3) + C, where a=2, b=3, and k = 1/2. If their form involves division by k, k=2 instead.

Analyzing two possible forms of the solution

The user might be dealing with two potential forms of the antiderivative for f(x) = sin(2x+3). For one form, F(x) = -cos(ax+b)/k + C, we get a

Thought for 16s