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Integrate formula document

in this video we're going to go over a few indefinite integral problems so what is the integral of 4 DX what is the answer for this problem the antiderivative of a constant all you need to do is just add an X to it this is going to be 4x and you also need to add a C value anytime the integrated function is always going to be a constant they need to add to it now the derivative of 4x is 4 the derivative of any constant is 0 so that's why you always need to add the constant so what about let's say the antiderivative of PI let's say it's dy instead of DX all you need to do is add a Y variable to it it's going to be pi times y plus C now what about the antiderivative of e DZ YZ a constant so it's just going to be e times E Plus e now the next type of problem that you're going to see is when you need to integrate a variable raised to a constant let's say X raised to the N this is equal to X raised to the N plus 1 divided by n plus 1 plus C so for example let's say if we wish to find the antiderivative of x squared DX this is equal to X to the third divided by 3 plus C the antiderivative of X to the third is X to the fourth divided by 4 plus C try this one what is the antiderivative of 8 X cube so focus on X to the third power the 8 is just going to come along for the ride the antiderivative of X to the third is X to the fourth divided by 4 and now we get simplified 8 divided by 4 is 2 so the final answer is 2x to the fourth plus C try this one what is the antiderivative of 5x to the sixth power so using the same technique let's add one to the exponent and then divide by that result so this is the answer now what about this expression what's the antiderivative of 7x DX well there is an invisible one so we can use the same technique if we add one it's going to be two and then divide by it plus C so the antiderivative of 3x is simply 3x squared divided by 2 plus C what if we have a polynomial function x squared minus 5x plus 6 so you need to integrate each one separately the antiderivative of x squared is X to the third divided by three and four five X is going to be five x squared divided by two and then if you have a constant just add a variable to it so this is the answer for each of these problems before I begin feel free to pause the video and work on it so try this one 4x cubed...