Question

How do you integrate `int (x^3-4x+2)dx`?

Answer 1

`x^4/4-2x^2+2x+C.`

Explanation:

Recall that `intx^ndx=x^(n+1)/(n+1)+c_1, n!=-1,`and, for a constant `k`,

`int[kf(x)+-g(x)]dx=kintf(x)dx+-intg(x)dx+c_2.`

Hence, the reqd. Integral`=intx^3dx-4intx^1dx+2intx^0dx`

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

`=x^4/4-2x^2+2x+C.`