Question

integrate(cos x cos 2x cos 3x) dx​

Answer 1

Answer:

I=∫cosx⋅cos2x⋅cos3xdx

=∫

2

1

(2cosx⋅cos3x)cos2xdx

=∫

2

1

(cos4x+cos2x)cos2xdx

=∫

2

1

(cos4x⋅cos2x+cos

2

2x)dx

=∫

4

1

(2cos

4

x⋅cos2x+2cos

2

2x)dx

=

4

1

∫(cos6x+cos2x+2cos

2

2x)dx

=

4

1

∫(cos6x+cos2x+cos4x+1)dx

=

4

1

[

6

sin6x

+

2

sin2x

+

4

sin4x

+x]❤️❤️