Question

How do you integrate `int (2x-3x^2)dx`?

Answer 1

`:. int(2x-3x^2)dx = x^2 - x^3 + C`

Explanation:

You should learn the power rule for integration, which is the opposite of that for differentiation, ie

`int x^ndx = x^(n+1)/(n+1) AA x in RR, x !=-1`

So `int(2x-3x^2)dx = 2x^(1+1)/(1+1)-3x^(2+1)/(2+1) + C`
`:. int(2x-3x^2)dx = 2x^2/2-3x^3/3 + C`
`:. int(2x-3x^2)dx = x^2 - x^3 + C`