antiderivative general

Question

Find the most general antiderivative for the function . 

dy/dx=4e^x+6

Answer 1

Antiderivatives have multiple answers if we don't know what the constant is. Usually we add a + C for this constant. Since your answer wants the most general answer, we assume C = 0.

integral (dy) = integral (4e^x + 6)dx

Break the integral into integral sums: y = integral (4e^x)dx + integral(6)dx

Use the constant integration rule: integral(ke^x)dx = k(integral(e^x)dx)

Use the exponential integral rule: integral(e^x)dx = e^x + C

Use the integral of a constant rule: integral(c)dx = cx + C

Apply the above rules to the integral: y = integral (4e^x)dx + integral(6)dx = 4e^x + 6x + C

Let C = 0

Answer: 4e^x + 6x