1. ## Antiderivatives

Alright, so we're supposed to find the anti derivatives for integration of 2t+e^2t.

The first anti derivative is 1/3t^3 + 1/2e^2t, but I am not certain how that was found, and then, we're supposed to find the anti derivative of that, and then the anti derivative once more.

I was wondering if someone could explain how exactly to find antiderivatives in a case like this?

2. Originally Posted by Mike5055
Alright, so we're supposed to find the anti derivatives for integration of 2t+e^2t.

The first anti derivative is 1/3t^3 + 1/2e^2t, but I am not certain how that was found, and then, we're supposed to find the anti derivative of that, and then the anti derivative once more.

I was wondering if someone could explain how exactly to find antiderivatives in a case like this?
I will be stunned if you don't you have these rules in your class notes or textbook:

$\int t^n \, dt = \frac{1}{n} t^{n+1} + C, ~ n \neq -1$.

$\int e^{kt} \, dt = \frac{1}{k} e^{kt} + C$.

You're expected to know them.