Mathematics - Calculus - Integral - Introduction to integrals - Integrals and Antiderivatives

10 steps: (1) The antiderivative F(x) of f(x) satisfies F'(x)=f(x). (2) Notation: ∫f(x)dx = F(x) + C. (3) The +C: since d/dx[constant]=0, we always add C. (4) Power rule reversed: ∫xⁿdx = x^(n+1)/(n+1) + C (n≠-1). (5) Example: ∫x³dx = x⁴/4 + C. Check: d/dx[x⁴/4] = x³ ✓. (6) ∫1/x dx = ln|x| + C (the