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(1)
∫sinx .cos(x/2) dx
=(1/2) ∫[sin(3x/2) +sin(x/2)] dx
=(1/2) [ -(2/3)cos(3x/2) -2cos(x/2)] +C
=-(1/3)cos(3x/2) -cos(x/2) +C
(2)
∫sin5x .cos7x dx
=(1/2) ∫ (sin12x -sin2x) dx
=(1/2)[ - (1/12)cos12x +(1/2)cos2x] +C
=-(1/24)cos12x + (1/4)cos2x + C
∫sinx .cos(x/2) dx
=(1/2) ∫[sin(3x/2) +sin(x/2)] dx
=(1/2) [ -(2/3)cos(3x/2) -2cos(x/2)] +C
=-(1/3)cos(3x/2) -cos(x/2) +C
(2)
∫sin5x .cos7x dx
=(1/2) ∫ (sin12x -sin2x) dx
=(1/2)[ - (1/12)cos12x +(1/2)cos2x] +C
=-(1/24)cos12x + (1/4)cos2x + C
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