1/2 ∫ln(1+2x)dx^2=?

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1/2∫ln(1+2x)dx^2=?1/2∫ln(1+2x)dx^2=?1/2∫ln(1+2x)dx^2=?1/2∫ln(1+2x)dx^2=1/2x^2ln(1+2x)-1/2∫x^2dln(1+2

1/2 ∫ln(1+2x)dx^2=?
1/2 ∫ln(1+2x)dx^2=?

1/2 ∫ln(1+2x)dx^2=?
1/2 ∫ln(1+2x)dx^2
=1/2x^2ln(1+2x)-1/2 ∫x^2dln(1+2x)
=1/2x^2ln(1+2x)- ∫x^2/(1+2x)dx
=1/2x^2ln(1+2x)- ∫(x^2-1/4+1/4)/(1+2x)dx
=1/2x^2ln(1+2x)- ∫[x/2-1/4+(1/4)/(1+2x)]dx
=1/2x^2ln(1+2x)-x^2/4+x/4-1/8ln(1+2x)+C

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1/2 ∫ln(1+2x)dx^2
=(1/2)[x^2ln(1+2x)- ∫2x^2/(1+2x) dx]
=(1/2)[x^2ln(1+2x)- (1/2)∫(4x^2-1+1)/(1+2x) dx]
=(1/2)[x^2ln(1+2x)- (1/2)∫(2x-1)+1/(1+2x) dx]
=(1/2)x^2ln(1+2x)- (1/4)(x^2-x)-(1/8)ln(1+2x) +C