Integral of e^kx
To find the integral of e^kx, we can follow these steps:
Step 1: Identify the variable of integration
In this case, the variable of integration is x
To find the integral of e^kx, we can follow these steps:
Step 1: Identify the variable of integration
In this case, the variable of integration is x.
Step 2: Use the power rule of integration
The power rule of integration states that if we have a function f(x) = x^n, then the integral of f(x) with respect to x is given by (1/(n+1)) * x^(n+1) + C, where C is the constant of integration.
Step 3: Apply the power rule to the function e^kx
In our case, the function f(x) = e^kx. Since the base e is a constant, we can treat it as a coefficient. Therefore, we can rewrite the function as f(x) = e^(k * x).
Now, we can apply the power rule. Since the exponent on e^kx is k, we add 1 to it to get k + 1. So, our integral becomes:
∫ e^kx dx = (1/(k + 1)) * e^(k * x) + C,
where C is the constant of integration.
Therefore, the integral of e^kx with respect to x is (1/(k + 1)) * e^(k * x) + C.
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