6.1 Series Expansion

• Definition & Notation
• Arithmetic Properties
• Riemann Sum

6.2 Integral Definition & Properties

• Definition & Notation
• Arithmetic Properties
• Integration by Parts

6.3 Exponentiation Integrals

• $\int x^n\thinspace dx$
• $\int (1/x)\thinspace dx$
• $\int b^{a·x}\thinspace dx$ & $\int e^{a·x}\thinspace dx$
• $\int \log_b x\thinspace dx$ & $\int \ln(x)\thinspace dx$

6.4 Common Trig Integrals

• $\int \sin(a·x)\thinspace dx$
• $\int \cos(a·x)\thinspace dx$
• $\int \csc(a·x)\thinspace dx$
• $\int \sec(a·x)\thinspace dx$
• $\int \tan(a·x)\thinspace dx$
• $\int \cot(a·x)\thinspace dx$
• $\int \sin^2(a·x)\thinspace dx$
• $\int \cos^2(a·x)\thinspace dx$
• $\int \csc^2(a·x)\thinspace dx$
• $\int \sec^2(a·x)\thinspace dx$
• $\int \tan^2(a·x)\thinspace dx$
• $\int \cot^2(a·x)\thinspace dx$
• $\int \sin^{–1}(a·x)\thinspace dx$
• $\int \cos^{–1}(a·x)\thinspace dx$
• $\int \csc^{–1}(a·x)\thinspace dx$
• $\int \sec^{–1}(a·x)\thinspace dx$
• $\int \tan^{–1}(a·x)\thinspace dx$
• $\int \cot^{–1}(a·x)\thinspace dx$

6.5 Advanced Trig Integrals

• $\int \sin^n(a·x)\thinspace dx$
• $\int \cos^n(a·x)\thinspace dx$
• $\int \csc^n(a·x)\thinspace dx$
• $\int \sec^n(a·x)\thinspace dx$
• $\int \tan^n(a·x)\thinspace dx$
• $\int \cot^n(a·x)\thinspace dx$
• $\int \sec^n(a·x)·\tan(a·x)\thinspace dx$
• $\int \csc^n(a·x)·\cot(a·x)\thinspace dx$
• $\int 1/(1±\sin(a·x))\thinspace dx$
• $\int 1/(1±\cos(a·x))\thinspace dx$
• $\int \sin(a·x)·\sin(b·x)\thinspace dx$
• $\int \sin(a·x)·\cos(b·x)\thinspace dx$
• $\int \cos(a·x)·\cos(b·x)\thinspace dx$
• $\int \sin^m(a·x)·\cos^n(b·x)\thinspace dx$ (sine reduction)
• $\int \sin^m(a·x)·\cos^n(b·x)\thinspace dx$ (cosine reduction)

6.6 Exponentiation & Trig Integrals

• $\int x^n·\sin(a·x)\thinspace dx$
• $\int x^n·\cos(a·x)\thinspace dx$

6.7 Integrals of $\sqrt{x^2+a^2}$ and $\sqrt{\pm x^2\mp a^2},\medspace a\isin\N$

• $\int \sqrt{x^2+a^2}\thinspace dx$
• $\int \sqrt{x^2-a^2}\thinspace dx$
• $\int \sqrt{a^2-x^2}\thinspace dx$
• $\int x·\sqrt{x^2+a^2}\thinspace dx$
• $\int x·\sqrt{x^2-a^2}\thinspace dx$
• $\int x·\sqrt{a^2-x^2}\thinspace dx$
• $\int x^2·\sqrt{x^2+a^2}\thinspace dx$
• $\int x^2·\sqrt{x^2-a^2}\thinspace dx$
• $\int x^2·\sqrt{a^2-x^2}\thinspace dx$
• $\int \sqrt{x^2+a^2}/x\thinspace dx$
• $\int \sqrt{x^2-a^2}/x\thinspace dx$
• $\int \sqrt{a^2-x^2}/x\thinspace dx$
• $\int \sqrt{x^2+a^2}/x^2\thinspace dx$
• $\int \sqrt{x^2-a^2}/x^2\thinspace dx$
• $\int \sqrt{a^2-x^2}/x^2\thinspace dx$
• $\int 1/\sqrt{x^2+a^2}\thinspace dx$
• $\int 1/\sqrt{x^2-a^2}\thinspace dx$
• $\int 1/\sqrt{a^2-x^2}\thinspace dx$
• $\int x/\sqrt{x^2+a^2}\thinspace dx$
• $\int x/\sqrt{x^2-a^2}\thinspace dx$
• $\int x/\sqrt{a^2-x^2}\thinspace dx$
• $\int x^2/\sqrt{x^2+a^2}\thinspace dx$
• $\int x^2/\sqrt{x^2-a^2}\thinspace dx$
• $\int x^2/\sqrt{a^2-x^2}\thinspace dx$
• $\int 1/x·\sqrt{x^2+a^2}\thinspace dx$
• $\int 1/x·\sqrt{x^2-a^2}\thinspace dx$
• $\int 1/x·\sqrt{a^2-x^2}\thinspace dx$
• $\int 1/x^2·\sqrt{x^2+a^2}\thinspace dx$
• $\int 1/x^2·\sqrt{x^2-a^2}\thinspace dx$
• $\int 1/x^2·\sqrt{a^2-x^2}\thinspace dx$

6.8 Improper Integrals

6.9 Sequences & Series

• Sequences
• Infinite Series
• Geometric Series
• Tests
  • Divergence
  • Integral
  • Ratio
  • Root
  • Comparison
• Alternating Series
• Power Series
• Taylor Series

6.A Parametric & Polar Integration

• Parametric Coordinates
• Polar Coordinates
• Conic Sections

6.B Complex Integration

• Definition
• Convolution
• Laplace Transform