1. ## Integration By Parts

Use integration by parts to find the integral:

2. Originally Posted by My Little Pony
Use integration by parts to find the integral:
for the first time, let $\displaystyle u = (\ln (4x))^2$ and $\displaystyle dv=dx$

and for the second time, let $\displaystyle u= \ln 4x$ and $\displaystyle dv=dx$

Integration by parts;

$\displaystyle \int u \, dv=uv - \int v \, du$

Function:
$\displaystyle \int(ln(4x))^2$

let $\displaystyle u=(ln(4x))^2$
$\displaystyle dv=dx$

$\displaystyle du=2(ln(4x))\frac{1}{4x}$
$\displaystyle v=x$

=$\displaystyle x(ln(4x))^2-\int2x(ln(4x))\frac{1}{4x}$

Then simplify the remaining integral and integrate once again

4. Originally Posted by Mr. Engineer
Integration by parts;

$\displaystyle \int u \, dv=uv - \int v \, du$

Function:
$\displaystyle \int(ln(4x))^2$

let $\displaystyle u=(ln(4x))^2$
$\displaystyle dv=dx$

$\displaystyle du=2(ln(4x))\frac{1}{4x}$
$\displaystyle v=x$

=$\displaystyle x(ln(4x))^2-\int2x(ln(4x))\frac{1}{4x}$

Then simplify the remaining integral and integrate once again
Are you sure it's 1/4x and not 1/x?