fan Posted January 31, 2011 Report Share Posted January 31, 2011 I normally get integration but this one really is killing me,x^4(x+1)^4(2x+1) integrate it using substitution.Your help will be greatly appreciated Reply Link to post Share on other sites More sharing options...
genepeer Posted January 31, 2011 Report Share Posted January 31, 2011 f(x) = x4(x+1)4(2x+1) = (x(x+1))4(2x+1)u = x(x+1)du/dx = 2x+1dx = du/(2x+1) Note: I'll use || as the integral sign|| f(x) dx = || x(x+1))4(2x+1) dx = || u4(2x+1) du/(2x+1) = || u4 du = u5/5 + c = 1/5*x5(x+1)5 + cFor substitution, it is advised, probably a must, to substitute the function inside a function. In this case my first attempt was u = x+1, since the outside function was "power 4". It didn't work. "Extract/Remove/Combine the powers" and the inside function becomes x(x+1). Using u = x(x+1) solves it! 1 Reply Link to post Share on other sites More sharing options...
fan Posted January 31, 2011 Author Report Share Posted January 31, 2011 ya i guess that was my problem i was also trying to substitute u = x +1.. I get it now Reply Link to post Share on other sites More sharing options...
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