Integration by parts anyone

I am having a little trouble solving a couple of integration by parts problems, mostly because I'm not sure which to use for u and which for dv, any help will be much appreciated.

Integral of (ln^2 x dx)

Integral of (xe^(2x)dx)

1.) ∫ln²(x) dx

u = ln²(x)

dv = dx

v = x

du = 2*ln(x)/x dx

uv - ∫v du

x*ln²(x) - ∫2*ln(x) dx

x*ln²(x) - 2x*ln(x) + 2*x + C

2.) ∫x*e^(2x) dx

Hint: let u = x and dv = e^(2x) dx

FOR SOLING IBP ALWAYS USE LIATE ORDER ie LOG.INVERSE TRIGO , ALGEBRAIC , TRIGONOMETRIC , EXPONENTIAL -USE u AS THAT FUNC WHICH COMES FIRST IN THE LIST N V AS THAT ONE WHICH COMES SECOND ! :D

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im guessing you mean ln(2x)
let f = ln(2x)
f' = 1/x

g'= 1
g = x

therefore

INT ln(2x)dx = xln(2x) - INT (1/x)(x)dx

I'm sure you know where to go from then

Here is the Integral of (xe^(2x)dx)

(x)((1/2)e^(2x)) - ((1/4)e^(2x)) + C