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How To Integrate eSign in Jitterbit

in this video we're going to focus on integrating exponential functions so let's go ahead and begin what is the antiderivative of e 3x DX we think the answer is for this function it's simply going to equal the same thing it's e to the X plus C now what about this one what is the antiderivative of e to the 2x DX this is going to be e to the 2x divided by the derivative of 2x which is 2 plus C that technique works only if you divided by constant if you divided by a variable it's not going to work so what do you think the answer for this one is e to the negative 5x DX it turns out that it's going to be the same thing e to the negative 5x divided by the derivative of negative 5 X which is negative 5 so let's see now let's prove the last one using u substitution so let's make u equal to a negative 5 X D U is the derivative of negative 5 X which is negative 5 times DX and solving for DX it's D U divided by negative 5 X so now let's replace negative 5 X with the u variable and let's replace a DX with D u over negative 5 now let's take the constant negative 5 and let's move it to the front so it's negative 5 antiderivative of EU or e to the U vu now we know that the integration of e to the X is simply e to the X so the antiderivative of e to you is simply e to u plus C and now we can replace you with negative 5x to the final answer oh by the way this should be a negative 1 over 5 because the 5 is on the bottom so just keep that a month I almost forgot about that but the final answer is negative run over 5 e to the negative 5x plus C which is the same thing as what we have which was e to negative 5x divided by negative 5 plus C is another one X Q times e raised to be X to the fourth DX go ahead and integrate the function so we can integrate by a substitution let's replace U with X to the fourth so there for a BU it's going to be the derivative of X to the fourth which is 4x cubed times DX and that would solve for DX that's d u over 4x cubed so let's replace X to the fourth with the you variable and now let's replace DX with D u over 4x cubed and so we could cancel X cubed now let's move the fourth to the front so it's 1/4 antiderivative e to udu the integration of e to the U is just e to the U times 1/4 plus C and now all I need to do is replace U with X...