antiderivatives

[mugzieee]

i dont understand how the antiderviative of 2 sin (2x) could be -cos(2x), what happens to the 2?

also how can the antiderivative of 5e^(5t) be e^(5t)?

[ek]

i dont understand how the antiderviative of 2 sin (2x) could be -cos(2x), what happens to the 2?

also how can the antiderivative of 5e^(5t) be e^(5t)?

Well, what do you get when you take the derivative of -cos2x? You apply the chain rule or whatever rule it is and come up with 2sin2x. Just like the 2 "appears" when taking the derivative, it also "disappears" when you take the antiderivative.

As for the second one, Dx (e^x) = e^x, that's why the second one is true.

If in doubt concerning an antiderivative, just check by taking the derivative of the answer you found.