Integrate Lnx1dx
Section a36 marks 5 7 short questions worth at most 8 marks each.
Integrate lnx1dx. Theory to dierentiate a product of two functions of x one uses the product rule. D dx uv u dv dx du dx v where u ux and v vx. Cosx 2 2x dx. We know from above that it is in the right form to do the substitution.
Cosu du sinu c. And finally put ux. Dierential equations integrating factor method graham s mcdonald a tutorial module for learning to solve 1st order linear dierential equations. Many challenging integration problems can be solved surprisingly quickly by simply knowing the right technique to apply.
While finding the right technique can be a. Be on the lookout for expressions where the top line is almost the derivative of the bottom line. For example3 z x3 x4 1 dx 1 4 z 4x3 x4 1 dx 1 4 lnx4 1c. Fall 2013 math 152 exam i ervsion a solutions 1.
A let u xand dv cos4xdx. Then du dx and v 1 4 sin4x. Using the integration by parts for. Core 4 module revision sheet the c4 exam is 1 hour 30 minutes long and is in two sections.
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