What is the antiderivative of #x(x+1)#?

1 Answer
Jun 21, 2016

#F(x)=x^3/3+x^2/2+C#

Explanation:

Before attempting to integrate, the expression should be simplified by distributing #x# over #(x+1)#.

Thus,

#f(x)=x(x+1)#
#f(x)=(x*x)+(x*1)#
#f(x)=x^2+x#

Integrating #f(x)#, we obtain the following:

#F(x)=intf(x)dx#
#F(x)=int(x^2+x)dx#
#F(x)=x^(2+1)/(2+1)+x^(1+1)/(1+1)+C#
#F(x)=x^3/3+x^2/2+C#

Note: Finding the anti-derivative of a function is the same as integration.