This is a graph of the function ln(x) (black) and the integral of ln(x) (red). I used the Runge Kutta 4 method to integrate the function from the left hand boundary, to the right hand boundary Here is a grand list of functions, and their respective integrals (family of functions so we add + C), you can switch to: 0. dy/dx = ln(x) | y = x*ln(x) - x + C 1. dy/dx = x^2 {x > 0} | y = x^3/3 + C {x>0} 2. dy/dx = e^x-0.2. | y = e^x - 0.2x + C 3. dy/dx = e^x | y = e^x + C 4. dy/dx = 2^x. | y = 2^x/ln(2) + C 5. dy/dx = 10^x. | y = 10^x/ln(10) + C. 6. dy/dx = sin(x). | y = -cos(x) + C. 7. dy/dx = cos(x). | y = sin(x) + C. 8. dy/dx = sin(2x). | y = -cos(x)/2 + C. 9. dy/dx = sinh(x). | y = cosh(x) + C. 10. dy/dx = cosh(x). | y = sinh(x) + C. 11. dy/dx = tanh(x). | y = ln(cosh(x)) + C.
I have read various articles on wikipedia and seen examples of the Runge-Kutta 4 method implemented in code to create a scratch prototype (might be the first) .
