Trig Integrals and Substitution

Half Angle Identities

• U-sub m and n are neither odd

• sin²(x) = (1-cos(2x))/2

• cos²(x) = (1+cos(2x))/2

n is odd and m is even

integral of : sin^m(x)cosⁿ(x)
u = sin(x), du = cos(x)

m is odd

integral of : sin^m(x)cosⁿ(x)
u = cos(x), du = sin(x)

Double Angle theorem

sin(2x) = 2sin(x)cos(x)

asin(theta)

Trig Expression substitute

atan(theta)

Trig Expression substitute

asec(theta)

Trig Expression substitute

sin²(x) + cos²(x) = 1

Pythagorean identity with sin and cos

1+tan² = sec²(x)

Pythagorean identity with tan and sec

1+cot²(x) = csc²(x)

Pythagorean with csc and cot

n is even

integral of : tan^m(x)secⁿ(x)

• u = tan(x)

• du = sec²(x)
  

m and n are odd

integral of : tan^m(x)secⁿ(x)

• u = sec(x)

• du = sec(x)tan(x)