Basic Integration Formulas

This set of flashcards covers basic integration formulas, useful for calculus review.

Basic integration formula for a constant

= kx + C, where k is any constant.

Integration of x^n

(x^(n+1))/(n+1) + C, for n ≠ -1.

Integration of 1/x

= ln|x| + C.

Integration of e^x

= e^x + C.

Integration of a^x

= a^x/lna +c for a > 0, a ≠ 1.

Integration of sin x

= -cos x + C.

Integration of cos x

= sin x + C.

Integration of sec^2 x

= tan x + C.

Integration of csc^2 x

= -cot x + C.

Integration of sec x tan x

= sec x + C.

Integration of csc x cot x

= -csc x + C.

*Integration of tan x

= ln|sec x| + C.

*Integration of cot x

= ln|sin x| + C.

*Integration of sec x

= ln|sec x + tan x| + C.

*Integration of csc x

= -ln|csc x + cot x| + C.

Integration of sinh x

= cosh x + C.

Integration of cosh x

= sinh x + C.

Integration of 1/√(a^2 - x^2)

= arcsin(x/a) + C.

Integration of 1/(a^2 + x^2)

= (1/a) arctan(x/a) + C.

Integration of 1/x√(x^2 - a^2)

= (1/a) arcsec(|x|/a) + C.

Integration of 1/√(a^2 +x^2)

= sinh^-1 (x/a) + C.

Integration of 1/√(x^2 - a^2)

= cosh^-1(x/a) + C.