calculus
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int e^5xsin3xdx =

Graham
∫ e^(5x) sin(3x) dx
=(i/2)∫ e^(5x) (e^(3ix)e^(3ix)) dx
=(i/2)∫ e^((53i)x)e^((5+3i)x) dx
=(i/2)((5+3i)e^((53i)x)/34(53i)e^((5+3i)x)/34) + C
= (5i/78)e^(5x)(e^(3ix)e^(3ix))+(3/78)e^(5x)(e^(3ix)+e^(3ix)) + C
= (5/34)e^(5x)sin(3x)  (3/34)e^(5x)cos(3x)
= e^(5x)(5sin(3x)3cos(5x))/34
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