integration

Asked by Kirandoon | 8th Jan, 2009, 09:01: PM

Expert Answer:

(sin4x / sinx) dx

= (4 sinx cosx cos2x) dx /sinx

= 4 cosx cos2x dx

=2 (cos 3x + cos x) dx

= (2 sin 3x) / 3 + 2 sinx+c

 

The following formula has been applied to get the 3rd step:

2 cos A cos B = cos (A+B) + cos (A-B)

Hence, 2cosx cos2x = cos (x+2x) + cos(x-2x) = cos 3x + cos(-x) = cos3x + cos x

Answered by  | 9th Jan, 2009, 12:35: PM

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