exercise function of integral trigonometry

Integral Functions Trigonometry:

1. ∫sinudu =  − Cosu + C
2. ∫cosu du = sinu + C
3. ∫sec2udu = tanu + C
4. ∫csc2udu =  − cotu + C
5. ∫secutanudu = secu + C
6. ∫cscucotudu =  − cscu + C
7. ∫tanudu =  − ln|cosu| + C
8. ∫cotudu = ln|sin.u| + C

Some form of integration of trigonometry

∫sinnxdx dan ∫cosnx dx

note: that completion of this form, if n is odd integer and positive number. After removing the factor sin x or cos x, then using equation:

sin2 + cos2x = 1, maka sin2x = 1 − cos2x dan cos2x = 1 − sin2x

Contoh :

1. Determine this example to function of integration of trigonometry

• ∫(sinx + cosx)dx

 = ∫sinxxdx + ∫cosxdx

 =  − cosx + sinx + C

 = ∫(3cosx − 2sinx)dx = 3∫cosxdx − 2∫sinxdx

 = 3.sinx − 2.( − cosx) = 3sinx + 2cosx + C

 = ∫(3cosx − 2sinx)dx = 3∫cosxdx − 2∫sinxdx

 = 3.sinx − 2.( − cosx) = 3sinx + 2cos + C

• ∫sin3xdx = ∫sin2xsinxdx

 = ∫(1 − cos2x)sinxdx

 =  − ∫(1 − cos2x)d(cosx)

 =  − cosx + 13cos3x + C