# Math Help - logarithmic integration help please

1. ## logarithmic integration help please

i'm scratching my head with this one:

evaluate the indefinite integral:

the integral of 2dx/(xln(5x))

so what i do is pull the 2 in front of the integral

use u-substitution

u=ln5x

du = 1/5x *5 dx = 1/x dx

so i get

2* integral of 1/u du

which gives me

2*lnu + C

and substituting back in gives me

2*ln(ln(5x))+C

but apparently thats not right . can anyone tell me where i'm going wrong?

2. Originally Posted by mthomas1
i'm scratching my head with this one:

evaluate the indefinite integral:

the integral of 2dx/(xln(5x))

so what i do is pull the 2 in front of the integral

use u-substitution

u=ln5x

du = 1/5x *5 dx = 1/x dx

so i get

2* integral of 1/u du

which gives me

2*lnu + C

and substituting back in gives me

2*ln(ln(5x))+C

but apparently thats not right . can anyone tell me where i'm going wrong?
I get the same answer as you and so does wolframalpha: integral of 2dx/(xln(5x)) - Wolfram|Alpha