Question

How do you evaluate the indefinite integral `int (x^2-2x+4)dx`?

Answer 1

`"A"(x)=1/3x^3-x^2+4x+"c"`

Explanation:

`intx^2-2x+4` `dx`

In order to evaluate this integral, apply the reverse power rule to each term separately.

Reverse power rule:

`intx^n` `dx=1/(n+1)x^(n+1)+ "constant"`

`intx^2-2x+4` `dx=1/3x^3-2/2x^2+4/1x+"c"`
`=1/3x^3-x^2+4x+"c"`