∫[e^(－2x)sinx/2]dx

∫[e^(-2x)sin½x]dx
= -½∫[sin½x]de^(-2x)
= -½[sin½x]e^(-2x) + ½∫e^(-2x)dsin½x + C
= -½[sin½x]e^(-2x) + ¼∫e^(-2x)cos½xdx + C
= -½[sin½x]e^(-2x) - ⅛∫cos½xde^(-2x) + C
= -½[sin½x]e^(-2x) - ⅛[cos½x]e^(-2x)-1/16∫e^(-2x)sin½xdx + C
=-(2/17)[4sin½x + cos½x]e^(-2x) + C

∫sin(x/2)d(e-2x)
=(e-2x)sin(x/2)-∫(e-2x)dsin(x/2)
=(e-2x)sin(x/2)-∫(e-2x)cos(x/2)d(x/2)
=(e-2x)sin(x/2)-(1/2)∫(e-2x)cos(x/2)dx
再乘以-1/2
所以=(-1/2)(e-2x)sin(x/2)+(1/4)∫(e-2x)cos(x/2)dx