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integral of ( ln(2x+1)dx)

im supposed to use by parts

heres what i have done

u=ln(2x+1)

du=2/2x+1

dv=dx

v=x

then i apply the formula uv-vdu

and i end up with another integral im supposed to use by parts for:

integral of(2x/2x+1 dx)

heres what i have done for that integral

u=2x

.5du=dx

dv=1/2x+1

v=ln(2x+1)

then i apply the formula again, and since i have the same integal i stared wit, i add it to the lef side etc etc... but i dont get the correct answer...what does it look lie im doing wrong?