Trig Integrals and substitution

sin2x =

2sinxcosx

sin²x + cos²x =

1

sec²x =

1 + tan²x

sin²x =

(1/2)(1 - cos2x)

cos²x =

(1/2)(1 + cos2x)

(a²-x²)^1/2, x =

asin0

(x²+a²)^1/2, x =

atan0

(x²-a²)^1/2, x =

asec0

If sinx is odd, u =

cosx

If cosx is odd, u =

sinx

If secx is even, u =

tanx

If tanx is odd, u =

u = secx

If secx is odd and tanx is even, use

integration by parts

If sinx and cosx are even,

substitute to reduce the integrand to one in lower powers