Question

find integration x^4 log x dx


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Answer 1

Answer:

∫x log x dx = (x^2/2) log x -x^2/4 + c

Proof : Using integration by parts,

∫udv = uv - ∫vdu

In ∫ x log x dx,

take, u=logx => du= (1/x) . dx

∫dv=∫x dx => v=x^2/2

Now substituting,

∫x log x = logx (x^2/2) - ∫x ^/2 . (1/x) dx = logx (x^2/2) - (1/2)∫dx= (x^2/2) log x -x^2/4 + c