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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.wolfram.com/