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Integration of x(2x-1)^(7) dx by parts

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Transcript

for this problem we want to find the anti derivative of the integral of X times two X minus one race to the seventh power dx. Using integration by parts. Now. In integration by parts. Yeah, assume that this is equal to the integral of U D. V. So if we set u equal to X and DV equal to two X minus one race to the seventh power dx. Then we will get do you equal to dx and V equal to the integral of two X -1. Race to the 7th power. The X. Now this integral of U times DV. This is equal to U V minus the integral of V times D You Now since our V is still in integral form we will use substitution. So let’s say w equal to two X -1. We get dw equal to two dx. Which means that one half dw equals D. X. So then from here we will get V equal to the integral of W. Race to the seventh Power times one half VW. This is equal to 1/2 times w racist. Seven plus one or eighth power over seven plus one or eight. This gives us W which is two X -1. Raised to the 8th power over 16. And so this integral now becomes U…

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