Quick Reference Formulas
Power Rule: ∫ x^n = x^(n+1)/(n+1)
Trig: sin → -cos, cos → sin
Exp: e^x → e^x (same!)
Reciprocal: 1/x → ln|x|
Substitution: Let u = inside function
Parts: ∫ uv' = uv - ∫ u'v
Exam Examples
∫ (3x² + 2x + 1) dx = x³ + x² + x + C
∫ e^(2x) dx = (1/2)e^(2x) + C
∫ cos(3x) dx = (1/3)sin(3x) + C
∫ (x² + 1)/(x³ + 3x) dx = (1/3)ln\|x³ + 3x\| + C
Power Rule: ∫ x^n = x^(n+1)/(n+1)
Trig: sin → -cos, cos → sin
Exp: e^x → e^x (same!)
Reciprocal: 1/x → ln|x|
Substitution: Let u = inside function
Parts: ∫ uv' = uv - ∫ u'v
Exam Examples
∫ (3x² + 2x + 1) dx = x³ + x² + x + C
∫ e^(2x) dx = (1/2)e^(2x) + C
∫ cos(3x) dx = (1/3)sin(3x) + C
∫ (x² + 1)/(x³ + 3x) dx = (1/3)ln\|x³ + 3x\| + C
