Integral sin4x/sinxdx

Asked by rraj.15266 | 1st Nov, 2017, 08:14: PM

Expert Answer:

begin mathsize 16px style straight I space equals integral fraction numerator sin 4 straight x over denominator sinx end fraction dx
straight I space equals space integral fraction numerator 2 sin 2 xcos 2 straight x over denominator sin begin display style straight x end style end fraction dx
straight I space equals 2 space integral fraction numerator 2 sinxcosxcos 2 straight x over denominator sin begin display style straight x end style end fraction dx
straight I space equals space 2 integral 2 cos 2 xcosxdx
straight I space equals space 2 integral open square brackets cos open parentheses 3 straight x close parentheses plus cos open parentheses straight x close parentheses close square brackets dx space space space space space space space space space space space open square brackets 2 cosAcosB equals cos left parenthesis straight A plus straight B right parenthesis plus cos left parenthesis straight A minus straight B right parenthesis close square brackets
straight I space equals space 2 open parentheses fraction numerator sin begin display style 3 end style begin display style straight x end style over denominator 3 end fraction plus sinx close parentheses plus straight c

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Answered by Sneha shidid | 13th Dec, 2017, 04:51: PM