How do you integrate ln(2x)ln(2x)?

1 Answer
mason m
Nov 24, 2016

x(ln(2x)-1)+Cx(ln(2x)−1)+C

Explanation:

I=intln(2x)dxI=∫ln(2x)dx

We should use integration by parts in the absence of all other possible integration strategies. Integration by parts takes the form intudv=uv-intvdu∫udv=uv−∫vdu. For intln(2x)dx∫ln(2x)dx, let:

{(u=ln(2x),=>,du=2/(2x)=1/x),(dv=dx,=>,v=x):}

Thus:

I=uv-intvdu=xln(2x)-intx1/xdx

I=xln(2x)-intdx

I=xln(2x)-x

I=x(ln(2x)-1)+C

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