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ᵈ/dx (C)
0
ᵈ/dx (kx)
K
ᵈ/dx kf(x)
Kf’(x)
ᵈ/dx (xn)
nxn-1
ᵈ/dx (f(x)±g(x))
f’(x)±g’(x)
∫(f(x)±g(x))dx
∫f(x)± ∫g(x)
∫(0)dx
C
∫(K)dx
kx+c
∫kf(x)dx
k∫f(x)dx
∫(xn)dx
(xn+1)/(n+1) +c
ᵈ/dx (sin x)
cos x
ᵈ/dx (cos x)
-sin x
ᵈ/dx (tan x)
Sec2x
ᵈ/dx (cot x)
-csc2x
ᵈ/dx (sec x)
Sec x tan x
ᵈ/dx (csc x)
-csc x cot x
∫(sin x)dx
-cos x + c
∫(cos x)dx
sin x + c
∫(sec2 x)dx
tan x + c
∫(csc2 x)dx
-cot x + c
∫(sec x tan x)dx
sec x + c
∫(csc x cot x)dx
-csc x + c
ᵈ/dx eu
eu·u’
ᵈ/dx au
au · u’ · ln a
ᵈ/dx Ln u
1/U · u’
ᵈ/dx Logau
1/U · u’ · 1/ln a
ᵈ/dx arcsin u
u’/√ 1-u²
ᵈ/dx arccos u
-u’/√ 1-u²
ᵈ/dx arctan u
u’/1+u²
ᵈ/dx arccot u
-u’/1+u²
ᵈ/dx arcsec u
u’/|u|√ u²-1
ᵈ/dx arccsc u
-u’/|u|√ u²-1
∫1/√ a²-u² du
arcsin u/a + C
∫1/a²+u² du
1/aarctan u/a + C
∫1/u√ a²-u² du
1/aarcsec |u|/a + C
∫ tan u du
-ln|cos u| + C
∫ cot u du
ln|sin u| + C
∫ sec u du
ln|sec u + tan u| + C
∫ csc u du
-ln|csc u + cot u| + C
∫1/u du
ln|u| + C
∫au du
au · 1/ln a + C
∫eu du
eu + C
What is the Trig sub of a²-x²
x=asinθ
What is the Trig sub of a²+x²
x=atanθ
What is the Trig sub of x²-a²
x=asecθ