8.1-8.5 AP Calc BC Study Guide

integral of u dv =

uv - integral v du

dv is the..

most complicated factor that can be easily integrated

for cos x, sin x, e^x, etc…

you can use the tabular method

sin^2x + cos^2x =

1

tan^2x =

1+sec^2x

1 + cot^2x =

csc^2(x) =

PR: sin^2x =

(1-cos2x)/2

PR: cos^2x

(1+cos 2x)/2

power of sin is odd and positive

save sin factor, convert rest to cos

power of cos is odd and positive

save cos as a factor, convert rest to sin

powers are positive and even

power reducing algebra!

power of sec is positive and even

save a sec^2x factor, convert rest to tan

power of tan odd and positive

save a secxtanx factor, convert rest to sec

integral of (tanx) dx

-ln |cosx| + c

integral of secx dx

ln|secx + tanx| + C

dy/dx tanx

sec^2x

dy/dx secx

secxtanx

a^2-u^2

sin

a^2+u^2

tan

u^2-a^2

sec