1) ∫ ( 3e^x - sin x + 6√x - 2 / x + 5 / cos^2x) dx= 3∫e^x dx - ∫sin x dx + 6∫√x dx - 2∫(1/x) dx + 5∫(1/cos^2x) dx= 3e^x + cos x + 6 * (2/3)x^(3/2) - 2ln|x| + 5tan x + C
2) ∫ ( 2 sin (3-2x) + 3 cos (3x-2)) dx= -2∫sin(2x-3) dx + 3∫cos(3x-2) dx= -2(-1/2)cos(2x-3) + 3(1/3)sin(3x-2) + C= cos(2x-3) + sin(3x-2) + C
1) ∫ ( 3e^x - sin x + 6√x - 2 / x + 5 / cos^2x) dx
= 3∫e^x dx - ∫sin x dx + 6∫√x dx - 2∫(1/x) dx + 5∫(1/cos^2x) dx
= 3e^x + cos x + 6 * (2/3)x^(3/2) - 2ln|x| + 5tan x + C
2) ∫ ( 2 sin (3-2x) + 3 cos (3x-2)) dx
= -2∫sin(2x-3) dx + 3∫cos(3x-2) dx
= -2(-1/2)cos(2x-3) + 3(1/3)sin(3x-2) + C
= cos(2x-3) + sin(3x-2) + C