Power and Exponential:

• integral $x^n$ dx = x^$\frac{n+1}{(n+1)}$ + C (n != -1)
• integral 1/x dx = ln|x| + C
• integral $e^x$ dx = $e^x$ + C
• integral e^(ax+b) dx = $\frac{1}{a}$e^(ax+b) + C
• integral $a^x$ dx = $a^x$/ln(a) + C (a > 0, a != 1)

Trigonometric:

• integral sin(x) dx = -cos(x) + C
• integral cos(x) dx = sin(x) + C
• integral tan(x) dx = -ln|cos(x)| + C = ln|sec(x)| + C
• integral cot(x) dx = ln|sin(x)| + C
• integral sec(x) dx = ln|sec(x) + tan(x)| + C
• integral csc(x) dx = ln|csc(x) - cot(x)| + C = -ln|csc(x) + cot(x)| + C
• integral $sec^2$(x) dx = tan(x) + C
• integral $csc^2$(x) dx = -cot(x) + C
• integral sec(x)tan(x) dx = sec(x) + C
• integral csc(x)cot(x) dx = -csc(x) + C

Inverse Trigonometric:

• integral 1/sqrt(a^{2-x}^2) dx = arcsin$\frac{x}{a}$ + C
• integral $\frac{1}{a^2+x^2}$ dx = $\frac{1}{a}$arctan$\frac{x}{a}$ + C
• integral $\frac{1}{x*sqrt(x^2-a^2}$) dx = $\frac{1}{a}$arcsec(|x|/a) + C

Algebraic with Log/Inverse Trig Results:

• integral $\frac{1}{x^2-a^2}$ dx = $\frac{1}{2a}$ln|$\frac{x-a}{(x+a)}$| + C
• integral $\frac{1}{a^2-x^2}$ dx = $\frac{1}{2a}$ln|$\frac{a+x}{(a-x)}$| + C
• integral 1/sqrt(x^{2+a}^2) dx = ln|x + sqrt(x^{2+a}^2)| + C
• integral 1/sqrt(x^{2-a}^2) dx = ln|x + sqrt(x^{2-a}^2)| + C
• integral sqrt(a^{2-x}^2) dx = $\frac{x}{2}$sqrt(a^{2-x}^2) + ($a^2$/2)arcsin$\frac{x}{a}$ + C
• integral sqrt(x^{2+a}^2) dx = $\frac{x}{2}$sqrt(x^{2+a}^2) + ($a^2$/2)ln|x+sqrt(x^{2+a}^2)| + C
• integral sqrt(x^{2-a}^2) dx = $\frac{x}{2}$sqrt(x^{2-a}^2) - ($a^2$/2)ln|x+sqrt(x^{2-a}^2)| + C