Mastering Integration: The Secret to Solving ∫e^x dx

∫e^x dx

To integrate the function ∫e^x dx, we can use the natural logarithm function

To integrate the function ∫e^x dx, we can use the natural logarithm function.

The integral of e^x, ∫e^x dx, is given by e^x + C, where C is the constant of integration.

To understand why this is the case, let’s go through the steps of integration.

Step 1: Start with the function ∫e^x dx.
Step 2: Notice that the derivative of e^x is e^x. In other words, if you were to differentiate e^x with respect to x, you would get e^x.
Step 3: Using this relationship, we can reverse the process and find the integral ∫e^x dx by figuring out what function, when differentiated, gives us e^x.
Step 4: Since we know that the derivative of e^x is itself, we can conclude that the integral ∫e^x dx is e^x.
Step 5: Finally, since the constant of integration can be added to any integral, we include the constant C in the result. This constant accounts for any possible shifts in the graph of the function.

Therefore, the integral of e^x, ∫e^x dx, is e^x + C, where C is the constant of integration.

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