Calculus

Differentiation

• Derivatives by First Principles - Exact Rates of Change
• Derivatives of Polynomials by First Principles - Example 1
• Derivatives of Polynomials by First Principles - Example 2
• Using the Chain Rule of Differentiation - 3 Examples
• What's the derivative of (x-1)ln(x)? - Applying the Product Rule
• The Product Rule of Differentiation - Example x²tan(x)
• How to differentiate cos(x)/x²? - Applying the Quotient Rule
• How to find the Derivative of sec(x)
• The Quotient Rule of Differentiation - Example: Derivative of tan(x)
• How to Sketch or Graph Polynomials - Part 1 of 3
• Sketching Polynomials - Part 2 of 3
• How to Sketch or Graph Polynomials - Part 3 of 3

Integration

• How to Find Areas Under Curves - Part 1 of 2
• How to Find Areas Under Curves - Part 2 of 2
• How to find the Area between 2 Functions / Curves
• How to Find the Volume of a Revolved Solid about the x axis
• How to Integrate ln(x)
• Integral of tan(x)
• Integral of sin²x using the Half Angle Formula
• Integral of cos²x using the Half Angle Formula
• How do I integrate tan²x?
• Integral 3x²+8/x³+4x by Partial Fraction Decomposition
• Integration by u-Substitution - Example Definite Integral x(2-x)⁵
• Integrals of sin^m(x)cosⁿ(x) - even powers
• How to Integrate ∫sin³(x)cos⁴(x)dx
• How to Integrate ∫sin³(x)cos³(x)dx - odd powers
• Evaluating the integral ∫tan²(x)+tan⁴(x)dx
• How to evaluate integrals of tan^m(x)secⁿ(x)
• How to integrate ∫tan²(x)sin(x)dx
• Integral of 1/(a²+x²)
• Integration by Trigonometric Substitution Example 1: -3/sqrt(1-9x²)
• Integration by Trigonometric Substitution Example 2: sqrt(a²-x²)
• Integral of ∫dx/(x²+4x+5) by Trigonometric Substitution
• What is the anti-derivative of 4x/(x²+6)? Integration by u-Substitution
• The integral of (4x+3)/(x²+1) - Version 1
• The integral of (4x+3)/(x²+1) - Version 2
• Evaluating a Definite Integral - Example 1/(9+x²)
• Integration of sec(x)
• Integral of ∫sec³xdx
• How to integrate ∫cotx / [cos²x + cosx + 1] dx
• Integrals of ∫dx / [a + bcosx + csinx] using t = tan(x/2)
• Integral of ∫sec²xdx
• Integrals of powers of cos(x) - ∫cos⁶(x)dx
• How to integrate cos(x²) - The Fresnel Integral C(x)
• The Fresnel Integral S(x) - How to integrate sin(x²)
• The integral of cos²(x²) expressed as a sum of an infinite series