Trigonometric Integrals
Even Powers of sin x or cos x:
Apply the sine and cosine half-angle:

![]()


![]()





Odd Powers of sin x or cos x:
Relate sine and cosine using the formula:
![]()
![]()
![]()

![]()
![]()
![]()

![]()
![]()
![]()

With an Even and Odd Exponent:
The odd exponent becomes one even and one odd.
![]()
![]()
![]()
![]()
![]()

The change of variable can also be made t = sin x or t = cos x
![]()
![]()


![]()
![]()


![]()


![]()

![]()
Products of Type sin(nx) · cos(mx):
Products are transformed into sums:
![]()
![]()
![]()
![]()
![]()

![]()
![]()
![]()
![]()
![]()
![]()
![]()
![]()
cos (-4x) = cos 4x
![]()