intregate cosx cos2x cos3xdx
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4
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]+c
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