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Visits since  Oct 2002

Power of x.

xn dx = x(n+1) / (n+1) + C  (n  -1)

1/x 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

arcsin x dx = x arcsin x + (1-x2) + C

arccsc x dx = x arccos x - (1-x2) + C

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

Inverse Trigonometric Result
 

dx  (1 - x2)  = arcsin x + C     dx  x (x2 - 1)  = arcsec|x| + C     dx  1 + x2  = arctan 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

a f(x) dx = a f(x) dx (if a is constant)

f(x) + g(x) dx = f(x) dx + g(x) dx

f(x) dx = f(x) dx | (a b)

f(x) dx + f(x) dx = f(x) dx

f(u) du/dx dx = f(u) du (integration by substitution)