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calculus derivatives & integrals
mperroud

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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