Find ∫ x^2(ln(4x))dx
∫x2 ln(4x)dx
Firstly , identify this question as integration by parts. Therefore set one half as value 'u' and one as value 'dv'.
Here we will set u = ln(4x).
Therefore: du/dx = 1/4x . (4)
du = 1/x dx We then set dv = x2 dx
dv/dx = x2
v = x3/3
The formula for integration by parts is :
u.v - ∫v.du
= ln(4x).(x3) - ∫(x3/3)(1/x)dx
= x3ln(4x) - ∫(x2/3)dx
= x3ln(4x) - x3/9 + c
SF
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