Question

Integral 8 sin 5x cos 3x dx

Answer 1

Int 8 sin(5x)cos(3x) dx
= 4 int 2 sin(5x) cos(3x) dx
= 4 int (sin(5x + 3x) + sin(5x - 3x)) dx
= 4 int (sin(8x) + sin(2x)) dx
= 4 (-1/8 cos(8x) - 1/2 cos(2x)) + c
= - 1/2 cos(8x) - 2 cos(2x) + c