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Calculus Formulas
Integrals and Derivatives
35
Mathematics
03/25/2010

Term
 ∫kf(u)=?
Definition
 k∫f(u)du
Term
 ∫du=?
Definition
 u+C
Term
 ∫du/u=?
Definition
 ln[u]+C
Term
 ∫a^udu=?
Definition
 (1/ln[a])a^u+C
Term
 ∫cos(u)du=?
Definition
 sin(u)+C
Term
 ∫cot(u)du=?
Definition
 ln[sin(u)]+C
Term
 ∫csc(u)du=?
Definition
 -ln[csc(u)+cot(u)]+C
Term
 ∫csc^2(u)du=?
Definition
 -cot(u)+C
Term
 ∫csc(u)cot(u)du=?
Definition
 -csc(u)+C
Term
 ∫[f(u)±g(u)]du=?
Definition
 ∫f(u)du±∫g(u)du
Term
 ∫u^ndu=?
Definition
 u^n+1/n+1+C n≠-1
Term
 ∫e^udu=?
Definition
 e^u+C
Term
 ∫sin(u)du=?
Definition
 -cosu+C
Term
 ∫tan(u)du=?
Definition
 -ln[cos(u)]+C
Term
 ∫sec(u)du=?
Definition
 ln[sec(u)+tan(u)]+C
Term
 ∫sec^2(u)du=?
Definition
 tan(u)+C
Term
 ∫sec(u)tan(u)du=?
Definition
 sec(u)+C
Term
 d/dx [cu]=?
Definition
 cu'
Term
 d/dx [u±v]=?
Definition
 u'±v'
Term
 d/dx [uv]=?
Definition
 uv'+vu'
Term
 d/dx [u/v]=?
Definition
 vu'-uv'/v^2
Term
 d/dx [c]=?
Definition
 0
Term
 d/dx [u^n]=?
Definition
 nu^n-1u'
Term
 d/dx [x]=?
Definition
 1
Term
 d/dx [abs(u)]=?
Definition
 u/abs(u) x (u') u≠0
Term
 d/dx [ln(u)]=?
Definition
 u'/u
Term
 d/dx [e^u]=?
Definition
 e^u x u'
Term
 d/dx [loga(u)]=?
Definition
 u'/(ln[a])u
Term
 d/dx [a^u]=?
Definition
 (ln[a])a^u x u'
Term
 d/dx [sin(u)]=?
Definition
 (cos[u])u'
Term
 d/dx [cos(u)]=?
Definition
 -(sin[u])u'
Term
 d/dx [tan(u)]=?
Definition
 (sec^2[u])u'
Term
 d/dx [cot(u)]=?
Definition
 -(csc^2[u])u'
Term
 d/dx [sec(u)]=?
Definition
 (sec[u]tan[u])u'
Term
 d/dx [csc(u)]=?
Definition
 -(csc[u]cot[u])u'
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