Standard Integrals

Standard integrals (must memorize): (1) ∫xⁿ dx = x^(n+1)/(n+1) + C; (2) ∫eˣ dx = eˣ + C; (3) ∫aˣ dx = aˣ/ln a + C; (4) ∫(1/x) dx = ln|x| + C; (5) ∫sin x dx = -cos x + C; (6) ∫cos x dx = sin x + C; (7) ∫sec² x dx = tan x + C; (8) ∫(1/√(1-x²)) dx = arcsin x + C. Example: ∫(3x² + 2x + 1) dx = x³ + x² + x + C. Shortcuts: Create integral table. Use substitution for complex forms. Exam tip: Memorize top 8 integrals. Verify by differentiating. Practice: Various function types and combinations.