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I often need to solve a type of integral which is :

$$\int x \ \sin ( n_1 x) \ \sin (n_2 x) \ dx $$ $n_1$ and $n_2$ are integers.

where the $n_1 $ and $n_2$ are the integer number. The way I solve this integral is to break down the $\sin n_1 x \sin n_2 x $ first using formula $\cos C - \cos D$ and then take the partial integration.

Is there any easy way to solve this integral?

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  • 3
    $\begingroup$ You already have the best way to integrate this function. No easier way! $\endgroup$ – Kavi Rama Murthy Aug 12 at 9:54
  • $\begingroup$ You can generalise this method to arbitrary $n_1$ and $n_2$ to get this result from Wolfram Alpha. $\endgroup$ – Toby Mak Aug 12 at 9:54
  • $\begingroup$ Listen to @KaviRamaMurthy $\endgroup$ – Kevin Nivek Aug 13 at 10:17

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