The coefficient 4 is the derivative of the exponent 4*x*: 4*e*^{4x}. Let *u* = 4*x*. Then the derivative of *u* with respect to *x* is 4. In symbols, Thinking of as a fraction and multiplying both sides by *dx*, we can write *du* = 4*dx*.
Now we can rewrite the integral using *u* instead of *x*. We know that Putting the original variable back in, we have *e*^{4x} + *C*.
We conclude that |