Maqboole Posted March 1, 2008 Share Posted March 1, 2008 Intergrate by parts: ∫ x(x +1)^4 dx X . ∫( x+1)^4 - ∫(∫(x+1)^4) . dy/dx (x) X. (X+1)^5 /5 - ∫(x+1)^5 /5 . 1 X. (X+1)^5 /5 – (x+1)^6 /30 +C. This is the best I can go. Our A’level teacher says its fine to do it till here, but the book has simplified answer I want to get to. Could someone tell me how to reach to the answer of (5X-1)(X+1)^5 /30 + C. Help appreciated ! Link to comment Share on other sites More sharing options...
D H Posted March 1, 2008 Share Posted March 1, 2008 The first two terms have a common factor of [math](x+1)^5[/math]: [math] \begin{split} x(x+1)^5/5 - (x+1)^6/30 + C =& \;(x+1)^5\left(\frac x 5 - \frac{x+1}{30}\right) +C \\ =& \;(x+1)^5\frac{(6x - (x+1)}{30} +C \\ =& \; \frac{(x+1)^5(5x - 1)}{30} +C \end{split} [/math] Link to comment Share on other sites More sharing options...
DeanK2 Posted June 19, 2008 Share Posted June 19, 2008 How do you use symbols? Link to comment Share on other sites More sharing options...
ydoaPs Posted June 19, 2008 Share Posted June 19, 2008 [math][/math] tags allow you to use LaTeX on the forum. Link to comment Share on other sites More sharing options...
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