# Shared Flashcard Set

## Details

Calculus: Integral Rules
Basic rules for integration
20
Mathematics
02/28/2011

Term
 int(k*f(u)du)
Definition
 k*int(f(u)du)
Term
 int([f(u)+/-g(u)]du)
Definition
 int(f(u)du)+/-int(g(u)du)
Term
 int(du)
Definition
 u+C
Term
 int(u^(n)du)
Definition
 u^(n+1)/(n+1)+C
Term
 int(du/u)
Definition
 ln|u|+C
Term
 int(e^(u)du)
Definition
 e^u+C
Term
 int(a^(u)du)
Definition
 a^(u)/ln(a)+C
Term
 int(sin(u)du)
Definition
 -cos(u)+C
Term
 int(cos(u)du)
Definition
 sin(u)+C
Term
 int(tan(u)du)
Definition
 -ln|cos(u)|+C
Term
 int(cot(u)du)
Definition
 ln|sin(u)|+C
Term
 int(sec(u)du)
Definition
 ln|sec(u)+tan(u)|+C
Term
 int(csc(u)du)
Definition
 -ln|csc(u)+cot(u)|+C
Term
 int((sec(u))^(2)du)
Definition
 tan(u)+C
Term
 int((csc(u))^(2)du)
Definition
 -cot(u)+C
Term
 int((sec(u)*tan(u))du)
Definition
 sec(u)+C
Term
 int((csc(u)*cot(u))du)
Definition
 -csc(u)+C
Term
 int(du/(a^(2)-u^(2))^(1/2))
Definition
 arcsin(u/a)+C
Term
 int(du/(a^(2)+u^(2)))
Definition
 (1/a)*arctan(u/a)+C
Term
 int(du/u*(u^(2)-a^(2))^(1/2))
Definition
 (1/a)*arcsec(|u|/a)+C
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