Tables of Integrals

Power of x.

xn dx = xn+1 (n+1)-1 + C (n -1)

x-1 dx = ln|x| + C

Exponential / Logarithmic

ex dx = ex + C	bx dx = bx / ln(b) + C
ln(x) dx = x ln(x) - x + C

Trigonometric

sin x dx = -cos x + C	csc x dx = - ln|csc x + cot x| + C
cos x dx = sin x + C	sec x dx = ln|sec x + tan x| + C
tan x dx = -ln|cos x| + C	cot x dx = ln|sin x| + C

Trigonometric Result

cos x dx = sin x + C	csc x cot x dx = - csc x + C
sin x dx = -cos x + C	sec x tan x dx = sec x + C
sec2 x dx = tan x + C	csc2 x dx = - cot x + C

Inverse Trigonometric

arc sin x dx = x arc sin x + (1-x2) + C

arc csc x dx = x arc cos x - (1-x2) + C

arc tan x dx = x arc tan x - (1/2) ln(1+x2) + C

Inverse Trigonometric Result

dx (1 - x2) = arc sin x + C dx x (x2 - 1) = arc sec|x| + C dx 1 + x2 = arc tan x + C

Useful Identities arccos x = /2 - arcsin x (-1 <= x <= 1) arccsc x = /2 - arcsec x (|x| >= 1) arccot x = /2 - arctan x (for all x)

Hyperbolic

sinh x dx = cosh x + C	csch x dx = ln |tanh(x/2)| + C
cosh x dx = sinh x + C	sech x dx = arctan (sinh x) + C
tanh x dx = ln (cosh x) + C	coth x dx = ln |sinh x| + C