Calculus 2 Trig Integration

Memorizing the stupid rules for trig integration plus trig identities

integral of sin^m(x) and m is odd

sub u=cos(x)

integral of cos^n(x) and n is odd

sub u=sin(x)

integral of sin^m(x) times cos^n(x), both n and m are odd

sub either cos(x) or sin(x)

integral of sin^m(x) times cos^n(x), both n and m are even

use cos²theta and/or sin²theta identities

sin(2theta)

2sinthetacostheta

cos(2theta)

cos²theta -sin²theta

cos²theta

1+cos(2theta)/2

sin²theta

1-cos(2theta)/2

integrak if the square root of (1+cos(nx)

use the trig identity 2cos²x=(1+cos2x)

integral of tan^nx

write tan^nx= tan^n-2(x)tan²(x), use tan²(x) = sec²(x)-1, then sub u=tan(x)

integral of sec^n(x), n is odd

sec^n(x) = sec^n-2(x)sec²(x), use integration by parts where u = sec^n-2(x) and v’=sec²(x)

integral of sec^n(x), n is even

sec^n(x)=sec^n-2(x)sec²x, sub = tanx, use trig identity: sec²x=1+tan²x

integral if tan^m(x)sec^n(x), n is even

sub u=tanx

integral if tan^m(x)sec^n(x), m is odd

sub u=sec(x)

integral if tan^m(x)sec^n(x), n is odd, m is even

use tan²(x)=sec²(x)-1

integral if tan^m(x)sec^n(x), n is even, m is odd

sub either u=tan(x) or u=sec(x)

integral of sin(mx)sin(nx)

1/2[cos(m-n)x-cos(m+n)x]

integral of sin(mx)cos(nx)

1/2[sin(m-n)x+sin(m+n)x]

integral of cos(mx)cos(nx)

1/2[cos(m-n)x+cos(m+n)x]

integral of sec(x)

ln |sec(x)+tan(x)|+C

integral of sec²(x)

tan(x) + C