Dave's Math Tables: Table of Integrals (Math | Calculus | Integrals | Table Of)

Power of x.
 xn dx = x(n+1) / (n+1) + C  (n  -1)  Proof 1/x dx = ln|x| + C

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 Result
 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 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    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

Click on Proof for a proof/discussion of a theorem.

 To solve a more complicated integral, see The Integrator at http://integrals.com.