# Thread: help integrating

1. ## help integrating

What do I use for u, du, v, and dv?

integrate (x^3)lnx dx

2. Originally Posted by Morgan82
What do I use for u, du, v, and dv?

integrate (x^3)lnx dx
Here's a useful acronym in determining what to let u be when applying integration by parts:

L - ogarithms
I - nverse trig
P - polynomials
E - exponential
T - rig

Using this, what is u?

3. Originally Posted by Morgan82
What do I use for u, du, v, and dv?

integrate (x^3)lnx dx
for $\displaystyle \int vu' = uv - \int v'u$

make $\displaystyle v = x^3$

and $\displaystyle u' = \ln(x)$

Find v' and u

4. Are you sure? I think $\displaystyle v=\ln x$ would work better.

5. Originally Posted by Scott H
Are you sure? I think $\displaystyle v=\ln x$ would work better.
True $\displaystyle \frac{d}{dx} \left( \ln(x)\right) =\frac{1}{x}$

I meant to write that, thanks!

6. $\displaystyle \int x^3 \ln(x)\:dx$. Let $\displaystyle z=\ln(x)\implies dx=e^z\:dz$ to get $\displaystyle \int x^3\ln(x)\:\overbrace{\longmapsto}_{z=\ln(x)}\int z e^{4z}\:dz$. Easier now, huh?