integral of xsin(3x)cos(2x)

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∫ xsin(3x)cos(2x)dx

Solution

12 x(−15 cos(5x)−cos(x))−12 (−125 sin(5x)−sin(x))+C

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∫ xsin(3x)cos(2x)dx

Apply Integration By Parts: 12 x(−15 cos(5x)−cos(x))−∫ 12 (−15 cos(5x)−cos(x))dx

=12 x(−15 cos(5x)−cos(x))−∫ 12 (−15 cos(5x)−cos(x))dx

∫ 12 (−15 cos(5x)−cos(x))dx=12 (−125 sin(5x)−sin(x))

=12 x(−15 cos(5x)−cos(x))−12 (−125 sin(5x)−sin(x))

Add a constant to the solution

=12 x(−15 cos(5x)−cos(x))−12 (−125 sin(5x)−sin(x))+C

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+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
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integral of xsin(3x)cos(2x)

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