Basic Differentation/Integation Rules

ᵈ_/dx (C)

0

ᵈ_/dx (kx)

K

ᵈ_/dx kf(x)

Kf’(x)

ᵈ_/dx (xⁿ)

nx^n-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 e^u}

e^u·u’

ᵈ_{/dx a^u}

a^u · u’ · ln a

ᵈ_/dx Ln u

¹/_U · u’

ᵈ_/dx Log_au

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

∫a^u du

a^u · ¹/_{ln a} + C

∫e^u du

e^u + 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