Question

Please help!

Answer 1

put ln5x=t
d(ln5x)/dx=(1/5x)*5dx=dt
(1/x)*dx=dt

Answer 2

what about du and u?

Answer 3

@amistre64

Answer 4

gorv did a "t" substitution ...

Answer 5

@electrokid !
im glad you are online. could you check my work please?

Answer 6

np. what/where is your work?

Answer 7

u=xIn(5x)?

Answer 8

du= 1/5dx
1/5du=dx?

Answer 9

you mean \[u=\ln(5x)\\
du={1\over 5x}(5dx)\implies du={1\over x}dx
\]

Answer 10

@Dodo1, did you get it?

Answer 11

not 100%...
du =1/5x

Answer 12

no. check the differentiation I did
I used the chain rule.

We have to use chain-rule whenever you do not have "x" on its own

Answer 13

i have to use chain rule too... ok.

Answer 14

can i use poduct too?

Answer 15

since its XIn(5x)

Answer 16

unless you have to function of "x" multiplying, you do not use it.

Again, look at the substitution.

Answer 17

you have to make a substitution such that
the derivative of the substituion exists in the given funtion

Answer 18

if you do
\[
u=x\ln(5x)\\{\rm then}\\
{du\over dx}=x{1\over5x}(5)+\ln(5x)\\
\therefore du=[1+\ln(5x)]dx
\]
we do not have this in the given function. so we do not make this substitution

Answer 19

thank you and sorry i have to go but i will check this later tonight. if im stuck please help me again,
thank you,

Answer 20

I got 4 (xIn(5x) for the answer!

Answer 21

@electrokid

Answer 22

how? show your steps

Answer 23

\[
I=4\int {1\over u}du\\
I=4\ln|u|+C\\
I=4\ln|\ln(5x)|+C
\]

Answer 24

∫ 4/(x ln(5x)) dx

Factor out constants:
= 4 ∫ 1/(x ln(5x)) dx

For the integrand 1/(x ln(7x)), substitute u = ln(7x) and du = 1/x dx:
= 4 ∫ 1/u du

The ∫ of 1/u is ln(u):
= 4 ln(u) + C

Substitute back for u = ln(5x):
= 4 ln(ln(5x)) + C

Answer 25

i mean 5 not 7 sorry.

Answer 26

i entred it and tells me that the answer is wrong

Answer 27

@electrokid

Answer 28

check with the absolute value signs

Answer 29

| <=? i used it i will post the photo

Answer 30

the inside paranthesis
(5x)
not
5(x)

Answer 31

is there any siginificant difference about it?

Answer 32

Thank you, it worked

Answer 33

yes. the way the website interprets is different
ln5(x) = (ln of (5)) times x
ln(5x) = ln of (5 times x)

Answer 34

I got it! thank you,

Answer 35

yw