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List of Derivative and Integration Formulae:

Derivative:

Integration:

Algebraic Group d n x = nxn−1 dx

Algebraic Group R

xn dx =

xn+1 n+1

Trigonometric Group d sin x = cos x dx d cos x = − sin x dx d tan x = sec2 x dx d cot x = − csc2 x dx d sec x = sec x tan x dx d csc x = − csc x cot x dx

Trigonometric Group R

cos x dx = sin x

R

sin x dx = − cos x

R

sec2 x dx = tan x

R

csc2 x dx = − cot x

R

sec x tan x dx = sec x

R

csc x cot x dx = − csc x

Logarithmic and Exponential Group

Logarithmic and Exponential Group d x e = ex dx d x a = ax log a dx d 1 log x = dx x Inverse Trigonometric Group 1 d sin−1 x = √ dx 1 − x2 d −1 cos−1 x = √ dx 1 − x2 d 1 tan−1 x = dx 1 + x2 d −1 cot−1 x = dx 1 + x2 1 d sec−1 x = √ dx x x2 − 1 −1 d csc−1 x = √ dx x x2 − 1

R

ex dx = ex

R

ax dx =

ax log a

R 1 dx = log x x Inverse Trigonometric Group 1 √ dx = sin−1 x 1 − x2 R −1 √ dx = cos−1 x 1 − x2 R 1 dx = tan−1 x or − cot−1 x 1 + x2 R 1 √ dx = sec−1 x or − csc−1 x |x| x2 − 1 R


Derivatives and integration