What do I use for u, du, v, and dv? integrate (x^3)lnx dx
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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?
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
Are you sure? I think $\displaystyle v=\ln x$ would work better.
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!
$\displaystyle \int x^3 \ln(x)\:dx$. 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?
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