AP Calculus BC Integrals To Know, Love, & Cherish

These flashcards cover integral calculus concepts that are essential for AP Calculus BC, including definitions and standard integral results.

Integral of \sin(u) du

-\cos(u) + C

Integral of \cos(u) du

\sin(u) + C

Integral of \sec^2(u) du

\tan(u) + C

Integration by Parts formula

\int u dv = uv - \int v du

Integral of \sec(u)\tan(u) du

\sec(u) + C

Integral of \csc^2(u) du

-\cot(u) + C

Integral of \sec(u) du

\ln |\sec(u) + \tan(u)| + C

Integral of \csc(u) du

\ln |\csc(u) - \cot(u)| + C

Integral of \sin^2(u) du

\frac{u - \sin(u)\cos(u)}{2} + C

Integral of \cos^2(u) du

\frac{u + \sin(u)\cos(u)}{2} + C

Integral of \tan^2(u) du

\tan(u) - u + C

Integral of \cot^2(u) du

-\cot(u) - u + C

Integral of \frac{1}{1 + u^2} du

\tan^{-1}(u) + C

Integral of \frac{du}{\left\vert u\right\vert\sqrt{u^2 - 1}}

\sec^{-1}(u) + C

Integral of \frac{du}{a^2 + u^2}

\frac{1}{a}\tan^{-1}\left(\frac{u}{a}\right) + C

Integral of e^u du

e^u + C

Integral of \frac{1}{u} du

\ln |u| + C

Integral of \tan(u) du

\ln |\sec(u)| + C

Integral of \cot(u) du

\ln |\sin(u)| + C

Integral of \csc(u)\cot(u) du

-\csc(u) + C

Integral of \frac{1}{\sqrt{a^2 - u^2}} du

\sin^{-1}\left(\frac{u}{a}\right) + C

Integral of a^u du

\frac{a^u}{\ln(a)} + C

Integral of -\frac{1}{\sqrt{1 - u^2}} du

\arccos(u) + C

Integral of -\frac{1}{1 + u^2} du

\text{arccot}(u) + C

Integral of -\frac{1}{\sqrt{a^2 - u^2}} du

\arccos\left(\frac{u}{a}\right) + C