Intergration by parts

[Maqboole]

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 !

[D H]

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]

[DeanK2]

How do you use symbols?

[ydoaPs]

[math][/math] tags allow you to use LaTeX on the forum.