Questions: Determine the following. [ int 3 e^-2 x d x int 3 e^-2 x d x=square ]

Solution Steps

To solve the integral \(\int 3 e^{-2 x} \, dx\), we can use the method of integration by substitution. We will let \(u = -2x\), then \(du = -2dx\). This substitution will simplify the integral, allowing us to integrate with respect to \(u\).

We start with the integral we want to solve: \[ \int 3 e^{-2x} \, dx \]

Using integration techniques, we find that: \[ \int 3 e^{-2x} \, dx = -\frac{3}{2} e^{-2x} + C \] where \(C\) is the constant of integration.

Final Answer