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QUESTION

# What is the integral of e^(7x)?

It's 1/7e^(7x) What you want to calculate is: int e^(7x)dx

We're going to use .

Let u = 7x Differentiate (derivative) both parts: du = 7dx (du)/7 = dx Now we can replace everything in the integral: int 1/7 e^u du Bring the constant upfront 1/7 int e^u du The integral of e^u is simply e^u 1/7e^u And replace the u back 1/7e^(7x)

There's also a shortcut you can use: Whenever you have a function of which you know the integral f(x), but it has a different argument => the function is in the form f(ax+b) If you want to integrate this, it is always equal to 1/a*F(ax+b), where F is the integral of the regular f(x) function.

In this case: f(x) = e^x F(x) = int e^x dx = e^x a = 7 b = 0 f(ax+b) = e^(7x) =>  int e^(7x)dx = 1/a*F(ax+b) = 1/7*e^(7x)

If you use it more often, you will be able to do all these steps in your head. Good luck!