Question

please help !

Answer 1

\[\int\limits_{}^{}\frac{ 4dx }{ xIn(5x) }\]

Answer 2

indfinite integals

Answer 3

what u need help with? :)

Answer 4

just posted

Answer 5

oh im so sorry but i cant help you with that. im only 14 XP

Answer 6

this is another u substitution for u=ln(5x)

Answer 7

du is 1/5dx?

Answer 8

du = (5/x )dx

Answer 9

dx=1/5du?

Answer 10

you're missing the x,

dx=(x/5)du

Answer 11

you were right with the 1/5 though

Answer 12

I see. whats next step?

Answer 13

you substitute back into the integral: What will you get when you do that?

Answer 14

remember that u=ln(5x)
and dx=(x/5)du

Answer 15

this is the most confusing part!

Answer 16

i have no idea..

Answer 17

Well basically you just look at your integral, and wherever you find an ln(5x) you put an u, wherever you find an dx you put (x/5)du

Answer 18

i see so \[\int\limits_{}^{}=u,du?\]

Answer 19

\[4 \int\limits \frac{ 1 }{ x \ln(5x) }dx=4 \int\limits \frac{ 1 }{ xu }\frac{ x }{ 5 }du\]

Answer 20

I do not understand, how you fet 1/xu and x/5...

Answer 21

\[4 \int\limits\limits \frac{ 1 }{ x \ln(5x) }dx=4 \int\limits\limits \frac{ 1 }{ xu }\frac{ x }{ 5 }du=\frac{ 4 }{ 5 }\int\limits \frac{ 1 }{ u }du\]

Answer 22

(get)

Answer 23

when you do a substitute, you choose an approrpriate substitution that will simplify, when you do that however, you also need to to two substitutions, not one. One is the regular u-substitution and the other remaining one is for the differential dx

Answer 24

so what I did above is I set
u=ln(5x), that's why it disappear in th emiddle part of the equation in terms of u.
Now the differential dx is (x/5)du, so I also substituted that in the middle part of these equations above.

Answer 25

this can then be simplified to the very right hand side of it.

Answer 26

I see. why its 4/5 in the front now?

Answer 27

the 5 went in the denominator, so if you want to pull that out - and you can do that because it's only a constant - then you have to factor out a 1/5 of the quotient, 4 times 1/5 is equal to (4/5)

Answer 28

i got it!

Answer 29

whats next step? place u in to the equation?

Answer 30

you solve the very right hand side integral. So you simplified your integral by a lot, now you want to solve:

\[\frac{ 4 }{ 5 } \int\limits \frac{ 1 }{ u }du\]

Answer 31

ok,

Answer 32

we know du.. so we use du in order to solve that?

Answer 33

What do you get when you differentiate ln(x)?

Answer 34

1/x?

Answer 35

exactly, so, when you integrate you do the exact opposite right? You want to find a function which, when you differentiate it, turns out to be the same function of your integral.

So, if ln(x) differentiated turns out to be 1/x, then what is the integral of (1/u)

Answer 36

In u? but why differentiation of In x is matter?

Answer 37

just to demonstrate that it is independent of the variable, because you seemed to struggle with the integral above, if you didn't however then pardon me, I misunderstood, however you might want to just write the answer down then and back substitute for u :-)

Answer 38

thank you. it explains.
mmmmm... integral of 1/u... is In u?

Answer 39

exactly

Answer 40

woop! what do i do next?

Answer 41

you plug back u=ln(5x) into your result and you're done.

Answer 42

where do i plug u=ln (5x)?

Answer 43

ln(u)
u=ln(5x)
ln(ln(5x))

Answer 44

thank you very much!

Answer 45

you're very welcome