Antiderivatives of Common Functions

Flashcards covering the antiderivatives of various common functions.

f(x) = x^n, n != -1

Antiderivative: x^(n+1)/(n+1) + C

f(x) = 1/x

Antiderivative: ln|x| + C

f(x) = 1/(x ln(b))

Antiderivative: log_b(x) + C

f(x) = e^x

Antiderivative: e^x + C

f(x) = b^x

Antiderivative: b^x / ln(b) + C

f(x) = 1/sqrt(1 - x^2)

Antiderivative: arcsin(x) + C

f(x) = 1/(1 + x^2)

Antiderivative: arctan(x) + C

f(x) = sin(x)

Antiderivative: -cos(x) + C

f(x) = cos(x)

Antiderivative: sin(x) + C

f(x) = sec^2(x)

Antiderivative: tan(x) + C

f(x) = csc^2(x)

Antiderivative: -cot(x) + C

f(x) = sec(x)tan(x)

Antiderivative: sec(x) + C

f(x) = csc(x)cot(x)

Antiderivative: -csc(x) + C

f(x) = k

Antiderivative: kx + C