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=?](/uploads/image/z/5998121-17-1.jpg?t=1%2F2+%E2%88%ABln%281%2B2x%29dx%5E2%3D%3F)
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
=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