Integration Formulas and Integral Rules: Complete List
Every basic integration formula and integral rule: power, exponential, log, trig and inverse trig integrals, substitution, by parts and definite integrals.
Category: Integrals
Read article → Integration Formulas and Integral Rules: Complete List
Integrals Class 12: All Formulas, Methods and Solved Examples
Class 12 Integrals: standard formulas, substitution, partial fractions, integration by parts, special integrals and definite integral properties, solved.
Fundamental Theorem of Calculus (Parts 1 and 2) Explained
The Fundamental Theorem of Calculus links derivatives and integrals. Both parts explained with intuition, formulas and worked examples.
Improper Integrals: How to Tell If They Converge or Diverge
Improper integrals have infinite limits or infinite integrands. Learn the limit definition, the p-integral test, comparison, and 6 worked examples.
Partial Fraction Decomposition: Steps and Examples
How to integrate rational functions with partial fractions: distinct linear factors, repeated factors and irreducible quadratics, with worked examples.
Integration by Parts: Formula, Liate Rule and Examples
Integration by parts: ∫u dv = uv − ∫v du. How to choose u with LIATE, 6 worked examples (x·sin x, ln x, arctan x, eˣ·cos x) and the tabular method.
U-Substitution: Step-by-Step Method and Examples
U-substitution reverses the chain rule. A 5-step method for choosing u, 7 worked examples, definite integrals with changed limits, and common mistakes.
Integral of √(1−x²): Trig Substitution and the Semicircle
∫√(1−x²)dx = ½(x√(1−x²) + arcsin x) + C. Full trig substitution, the semicircle area π/2 shortcut, and the general √(a²−x²) formula.
Integral of sec²(x) = tan(x) + C, with Examples
The integral of sec²(x) is tan(x) + C, because the derivative of tan x is sec²x. Examples with sec²(3x), tan²x, and definite integrals.
Integral of x·e^x: Integration by Parts Step by Step
∫x·e^x dx = x·e^x − e^x + C. A clear integration by parts walkthrough with LIATE, x²e^x, x·e^(2x), x·e^(−x) and a definite integral.