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Quotient Rule

d/dx f(x)/g(x)
(f′g - fg′)/(g2)
Product Rule

d/d [f(x) • g(x)]
(f′g) + (fg′)
Power Rule

d/dx [g(x)]n
n[g(x)]n-1 • (g′)
d/dx (lnx)
1/x
d/dx (ex)
(ex)
d/dx (eax)
(aeax)
d/dx (ln f)
(f′/f)
d/dx (ef)
(ef) • (f′)
∫1/x dx
ln/x/ + C
∫Kdx
Kx + C
∫xn dx
xn+1
-------     + C
 n+1
∫eax dx
(1/a) eax + C
∫u dv
uv - ∫vdu
Integration by Parts

If   ∫xn eax dx
Choose

u= xn         dv= eax dx
Integration by Parts

If    ∫xn lnx dx
Choose

u= lnx   dv= xn dx
Integration by Parts

If     ∫(x + a)(x + b)n dx
Choose

u=(x+a)   dv=(x+b)n dx
x of y cards