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

Answer 1

Isaiah Allen

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

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.

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Answer 2

Emily Ammerman

The antiderivative of ( x(x+1) ) is ( \frac{1}{3}x^3 + \frac{1}{2}x^2 + C ), where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.