1. ## Integration by Parts

I'm sure how to go about solving this integral:

∫cos(ln(2x))dx

Could someone explain how to set it up to use integration by parts?

2. ## Re: Integration by Parts

Use $\displaystyle u=\text{ln}(2x)$

3. ## Re: Integration by Parts

Originally Posted by MaxJasper
Use $\displaystyle u=\text{ln}(2x)$
Okay, that'll give me du = 1/x dx which I cannot substitute back into the original equation.

4. ## Re: Integration by Parts

Originally Posted by Preston019
Okay, that'll give me du = 1/x dx which I cannot substitute back into the original equation.
$\displaystyle u = \ln(2x)$

$\displaystyle x = \frac{e^u}{2}$

$\displaystyle dx = \frac{e^u}{2} \, du$

substitute ...

$\displaystyle \int \cos(u) \cdot \frac{e^u}{2} \, du$

now perform the integration by parts ...

5. ## Re: Integration by Parts

Originally Posted by skeeter
$\displaystyle u = \ln(2x)$

$\displaystyle x = \frac{e^u}{2}$

$\displaystyle dx = \frac{e^u}{2} \, du$

substitute ...

$\displaystyle \int \cos(u) \cdot \frac{e^u}{2} \, du$

now perform the integration by parts ...
Oooooooohhh! Okay, that helped so much. Thanks!