∫ x (2x-1)^7

∫ x (2x-1)^7 integral by parts

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1 Answer

∫x(2x-1)⁷dx.

Let y=2x-1, dy=2dx, dx=dy/2; x=(y+1)/2.

∫((y+1)/2)y⁷(dy/2)=¼∫(y⁸+y⁷)dy=¼(y⁹/9+y⁸/8)+C.

So the integral is ¼(2x-1)⁸((2x-1)/9+⅛)+C=

¼(2x-1)⁸(2x/9-1/9+1/8)=¼(2x-1)⁸(2x/9+1/72)+C=

(1/288)(2x-1)⁸(16x+1)+C.

by Top Rated User (1.2m points)

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