Question

indefinite integral

Answer 1

so I think you should let u=ln(2x) right? but then I'm confused as where to go from there

Answer 2

then find du = 1/(2x) *2 dx...
and further..

Answer 3

does that work though? it seems like the x's wouldn't cancel...

Answer 4

du = 1/x * dx?

Answer 5

yes, you math is correct, but whether it helps simplify the integral is the question, I'm looking at it...

Answer 6

yeh I get what you mean, that's also part of the reason of why I'm confused

Answer 7

Are you familar with integration by parts?

Answer 8

sorry not really because my lecturers didn't explain it that well

Answer 9

well this problem works with integration by parts

i can tell you the formula
\[\int\limits_{}^{}udv = uv - \int\limits_{}^{} vdu\]

Answer 10

so we need to let u equal to something and dv equal to somethign

lets let u = ln(2x) and dv = 10x

Answer 11

so we just need to follow the formula but we are missing du and v

to find du we can just differetiate u
so du = 1/x

and to find v we just integrate dv
so v = 5x^2

understanding so far?

Answer 12

yeh but it should be du/dx = 1/x? not du =1/x?

Answer 13

sorry i missed out one part
du = 1/x (dx)

Answer 14

just multiple the dx on both sides

Answer 15

yep

Answer 16

it makes subsittuion easier

Answer 17

so anyways you have everything you need to find the integral

\[\int\limits_{}^{}10x \ln 2x dx = \ 5x^2ln 2x -\int\limits_{}^{}5x^2 (1/x)(dx) \]

Answer 18

so if you look at the integral at the right
it can simplify into
\[\int\limits_{}^{} 5xdx = \frac{ 5 }{ 2 } x^2\]

Answer 19

just put everythign together and your done

Answer 20

and dont forget to add a +C for the constant

Answer 21

∫10xln2xdx = 5x^2ln(2x) - 5/2x^2 + C

Answer 22

yup thats right

Answer 23

ok, let me try enter the answer.

Answer 24

it was correct.

Answer 25

I understand the maths side on how to do it but I'd probably need someone to explain it to me properly

Answer 26

integration by parts is pretty much the product rule in reverse

Answer 27

you if you are multiplying 2 functions then you can use the product rule to differentiate and you use integration by parts to integrate

Answer 28

ok, I 90% understand lol

Answer 29

just do more practice and you will understand it 100% :)

Answer 30

yeh I guess so lol, but thanks for the help jay

Answer 31

your welcome man glad to help