1/2 ∫ln(1+2x)dx^2=?
问题描述：
1/2 ∫ln(1+2x)dx^2=?
答
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
答
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...