Integration Formulas

Constant multiple

∫c • f(x)dx= c • ∫f(x)dx

Sum & Difference

∫[f(x) ± g(x)]dx = ∫f(x)dx ± ∫g(x)dx

Power rule

∫x^n dx = x^(n+1)/(n+1) +C

∫cosdx =

sinx +C

∫sec²xdx =

tanx +C

∫secxtanxdx=

secx +C

∫sinxdx =

-cosx+ C

∫csc²xdx =

-cotx+ C

∫cscxcotx =

-cscx +C

∫e^xdx=

e^x +C

∫(1/x)dx =

ln|x| +C

Fundamental Theorem of Calculus

Basically, you find the antiderivative [F(x)], and then define the function with the b and a values given [F(b) - F(a)].

∫tanxdx=

-ln|cosx| + C

∫secxdx =

ln|secx+tanx| +C

∫cotxdx

ln|sinx| + C

∫cscxdx

-ln|cscx+cotx| + C

∫dx/sqrt(1-x²)

arcsin(x/a) + C

∫dx/1+x²

1/A(arctan(U/A)) + C