Question

substitution problem
integration

Answer 1

\[\int\limits x(2x-1)^3 d\]

Answer 2

ok I just really need someone to tell me if I did this incorrect

Answer 3

i guess you tried u = 2x-1 ?

Answer 4

u=2x-1
dx=du/2
x=(u+1)/2

Answer 5

correct, so far

Answer 6

\[\int\limits (2x-1)^3 x dx\]
\[\int\limits (u^3)\left( \frac{ u+1 }{ 2 } \right)\left( \frac{ du }{ 2} \right)\]

Answer 7

\[\frac{ 1 }{ 4} \int\limits u^3(u+1) du\]

Answer 8

yep

Answer 9

ok I just expanded that and then integrated it

Answer 10

final answer ?

Answer 11

\[\frac{ 1 }{ 4 }\left[ \frac{ u^5 }{ 5}+\frac{ u^4 }{ 4 } \right]+C\]

Answer 12

then I just sub (2x-1) everywhere u is

Answer 13

absolutely correct :)

Answer 14

thanks

Answer 15

I think someone was helping me with this yesterday and it did not make sense until today when I redid it or did another similar problem. Thanks so much :)

Answer 16

welcome ^_^