MAT 129 - Basic Integration Rules (Table of Integrals)

Vocabulary flashcards covering the basic integration rules and common antiderivatives from the lecture notes.

Power Rule for Integrals

If n ≠ -1, ∫ u^n du = u^(n+1)/(n+1) + C.

Integral of e^u

∫ e^u du = e^u + C.

Integral of sin u

∫ sin u du = -cos u + C.

Integral of cos u

∫ cos u du = sin u + C.

Integral of sec^2 u

∫ sec^2 u du = tan u + C.

Integral of sec u tan u

∫ sec u tan u du = sec u + C.

Integral of tan u

∫ tan u du = -ln|cos u| + C (equivalently ln|sec u| + C).

Integral of sec u

∫ sec u du = ln|sec u + tan u| + C.

Integral of 1/u

∫ (1/u) du = ln|u| + C.

Integral of csc u cot u

∫ csc u cot u du = -csc u + C.

Integral of csc^2 u

∫ csc^2 u du = -cot u + C.

Integral of cot u

∫ cot u du = ln|sin u| + C.

Integral of csc u

∫ csc u du = ln| csc u - cot u | + C.

Integral of du / sqrt(a^2 - u^2)

∫ du / sqrt(a^2 - u^2) = arcsin(u/a) + C.

Integral of du / (a^2 + u^2)

∫ du / (a^2 + u^2) = (1/a) arctan(u/a) + C.

Integral of sinh x

∫ sinh x dx = cosh x + C.

Integral of cosh x

∫ cosh x dx = sinh x + C.