What is the indefinite integral of 2x ln2x dx

Answers:

ans:

this is more challenging!

OK, not revised this for a'while, so may go a bit wrong, but hopefully someone else will correct me if I do:

you want to know:

int(2xln(2x)dx

int(u.(dv/dx)dx) = u.v - int(v.(du/dx)dx)

so set dv/dx = 2x and u = ln(2x) this is because its easier to int 2x than ln(2x)

gives:

int(2x.ln(2x)dx) = x^2.ln(2x) - int(x^2.(1/x)dx)

= x^2.ln(2x) - int(xdx)

=x^2.ln(2x) - x/2
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