Effortlessly Solve Integrals: Learn the Derivative of Logarithmic Functions

[meee]

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

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