Tables



Power of x.

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xn dx = xn+1 (n+1)-1 + C
(n -1) Proof
x-1 dx = ln|x| + C

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Exponential / Logarithmic
ex dx = ex + C
Proof
bx dx = bx / ln(b) + C
Proof, Tip!
ln(x) dx = x ln(x) - x + C
Proof
Trigonometric
sin x dx = -cos x + C
Proof
csc x dx = - ln|csc x + cot x| + C
Proof
cos x dx = sin x + C
Proof
sec x dx = ln|sec x + tan x| + C
Proof
tan x dx = -ln|cos x| + C
Proof
cot x dx = ln|sin x| + C
Proof
Trigonometric ResultTables
cos x dx = sin x + C
Proof
csc x cot x dx = - csc x + C
Proof
sin x dx = -cos x + C
Proof
sec x tan x dx = sec x + C
Proof
sec2 x dx = tan x + C
Proof
csc2 x dx = - cot x + C
Proof
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 ResultTables
dx (1 - x2) = arcsin x + C
dxx (x2 - 1) = arcsec|x| + C
dx1 + 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)

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

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Tablespoon To Oz

Proof

Console Tables

for a proof/discussion of a theorem.
To solve a more complicated integral, see The Integrator at http://integrals.com.