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Calculus: Integral Rules
Basic rules for integration
20
Mathematics
11th Grade
02/28/2011
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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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