What is the integral of #(x^2)(lnx)#?

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Camille Share
Apr 21, 2015

#intx^2*ln(x)dx#

By part :

#f(x)=ln(x)#

#f'(x)=1/x#

#g(x)=1/3x^3#

#g'(x)=x^2#

#intx^2*ln(x)dx=[ln(x)*1/3x^3]-1/3int1/x*x^3dx#

#intx^2*ln(x)dx=[ln(x)*1/3x^3]-1/3intx^2dx#

We have :

#intx^2*ln(x)dx=[ln(x)*1/3x^3-1/9x^3]#

#intx^2*ln(x)dx=[3/9ln(x)*x^3-1/9x^3]#

Factorize :

#intx^2*ln(x)dx=1/9[3ln(x)*x^3-x^3]+C#

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