Question

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

Answer 1

`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.