Effortlessly Solve Integrals: Learn the Derivative of Logarithmic Functions

[meee]

\int \frac{1}{x\log_{e} 4x} dx<br /> <br />

wow i finally got latex to work

ok... so i did it on a text and got \log_{e}(\log_{e}4x)+c

now i did it and got \frac{1}{4}\log_{e}(\log_{e}4x)+c

which is right?

what is the derivative of \log_{e}4x ?

 

[courtrigrad]

do you mean \int \frac{1}{x\ln 4x} dx? Use the substitution u = \ln 4x.

 

[courtrigrad]

your first answer is correct. can you see why?

\log_{e} 4x = \ln 4x. Can you take the derivative of that now?

 

[meee]

your first answer is correct. can you see why?

\log_{e} 4x = \ln 4x. Can you take the derivative of that now?

ohhhh... is it \frac{4}{4x} = \frac{1}{x} ?

 

[courtrigrad]

yes it is.

 

[meee]

i see.. Thanks