Standard integrals
and derivatives




Integrand/derivative
Integral/differand

sec2  x tan  x




-cosec   x cot   x cosec  x

-sec   x tan   x sec  x

Derivative of cot x - cosec2  x cot  x




1/(1+x^2) arctan   x

-sec   x tan   x sec  x

Derivative of cot x - cosec2  x cot  x




Integral of tan x




Integral of cosec x

Integral of sec x

Integral of cot x


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Given these pairs (either differentiating down or, adding a constant of integration, integrating up)...
x^n, e^x etc.
... we illustrate some common results below...










Derivative of tan x
Derivative of tan x










Derivative of cosec x
Derivative of cosec x






Derivative of sec x
Derivative of sec x






Derivative of cot x
Derivative of cot x










Derivative of arctan x
derivative of arctan x






Derivative of arcsin x
Derivative of arcsin x






Derivative of arccos x
Derivative of arccos x










Integral of tan x
Integral of tan x










Integral of cosec x
Integral of cosec x






Integral of sec x
Integral of sec x






Integral of cot x
Integral of cot x






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