Evaluate (x^3 - 2x)dx?

differentiating:
apply rule: d/dx x^n=nx^(n−1)
3x^2−2

Integrating:
Apply rule: ∫x^n dx=[x^(n+1)]/(n+1) +C
x^4/4−x^2
Add constant
x^4/4−x^2+c

∫(x³ - 2x)dx

= ∫x³dx - ∫2xdx

= (x⁴/4) - 2(x²/2) + C

= (x⁴/4) - x² + C

∫ x³ - 2x dx = x^4 / 4 - x^2 + C

∫ (x^3-2x) dx
= ∫ x^3 dx -2 ∫ x dx
= (1/4) x^4 - 2 (1/2) x^2
= (1/4) x^4 - x^2 + C

Use the power rule for derivatives in reverse.
∫ (x^3 - 2x) dx =
x^4/4 - x^2 + c