Question

∫x(x-1)⁵ dx

Answer 1

i know u=(x-1) so du = 1dx

Answer 2

let u =x-1

differntiate that.

Then let x=u+1

Answer 3

ok got there.
so I subbed it back in and had ∫(u+1)(u)⁵ du

Answer 4

like now distibute (u)^5 into the parentheses

Answer 5

okay so I got:
∫(u⁶+u⁵) du

Answer 6

now just integrate

Answer 7

which = ∫u¹¹ du

Answer 8

or should i integrate before that?

Answer 9

you cant just add that like that

Answer 10

integrate u^6 and u^5 bythemselves

Answer 11

okay so I have:
1/7 (x-1)⁷ + 1/6(x-1)⁶

Answer 12

+ C

Answer 13

that looks good to me

Answer 14

the book has a diff. answer tho

Answer 15

i know I can pull (x-1)⁶ out to have:
(x-1)⁶ (1/7(x-1) + 1/6)

Answer 16

yeah we have to factor out some terms

Answer 17

(x-1)^5
----------
x (x-1)^6 /6
-1 (x-1)^7 /42
0


\[\frac{x(x-1)^6}{6} -\frac{(x-1)^7}{42}\]
maybe?

Answer 18

it works lol

http://www.wolframalpha.com/input/?i=d%2Fdx+%28x+%28x-1%29^6+%2F6++-%28x-1%29^7+%2F42%29

Answer 19

+C of course