Trigonometric Integration

1
Trigonometric Integration
1. Integrals of the form
Case 1 m is odd.
Remedy use the substitution u cos x
Case 2 n is odd.
Remedy use the substitution u sin x
2
Trigonometric Integration
1. Integrals of the form
Case 3 m n and both are even.
Remedy use the identity sin x cos x (sin2x)/2

Case 4 m and n are both even but unequal.
Remedy use the power reduction formulas
3
Trigonometric Integration
2. Integrals of the form
Case 1 n is even.
Remedy use the substitution u tan x and
the identity sec2x 1
tan2x
Case 2 m is odd.
Remedy use the substitution u sec x and
the identity tan2x sec2x 1
4
Trigonometric Integration
2. Integrals of the form
Case 3 n is odd and m is even.
Remedy use the identity tan2x sec2x 1 and
the reduction formula for integration of secmx
5
Trigonometric Integration
3. Integrals of the form
Remedy use the identity sinAcosB
sin(A B) sin(A B)/2
4. Integrals of the form
Remedy use the identity sinAsinB
cos(A B) cos(A B)/2
5. Integrals of the form
Remedy use the identity cosAcosB
cos(A B) cos(A B)/2