Power and Exponential:

• integral x^n dx = x^(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 = (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(x/a) + C
• integral 1/(a^2+x^2) dx = (1/a)arctan(x/a) + C
• integral 1/(x*sqrt(x^2-a^2)) dx = (1/a)arcsec(|x|/a) + C

Algebraic with Log/Inverse Trig Results:

• integral 1/(x^2-a^2) dx = (1/2a)ln|(x-a)/(x+a)| + C
• integral 1/(a^2-x^2) dx = (1/2a)ln|(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 = (x/2)sqrt(a^2-x^2) + (a^2/2)arcsin(x/a) + C
• integral sqrt(x^2+a^2) dx = (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 = (x/2)sqrt(x^2-a^2) - (a^2/2)ln|x+sqrt(x^2-a^2)| + C