求一道不定积分(简单)
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求一道不定积分(简单)
求一道不定积分(简单)
求一道不定积分(简单)
用积化和差
原式=-1/2∫(cos4x-cos2x)dx
=-1/2∫cos4xdx+1/2∫cos2xdx
=-1/8sin4x+1/4sin2x+C
∫ (sinx * sin3x) dx
= (1/2)∫ [cos(x - 3x) - cos(x + 3x)] dx
= (1/2)∫ cos2x dx - (1/2)∫ cos4x dx
= (1/2)(1/2)sin2x - (1/2)(1/4)sin4x + C
= (1/8)(2sin2x - sin4x) + C
sinA * sinB = (...
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∫ (sinx * sin3x) dx
= (1/2)∫ [cos(x - 3x) - cos(x + 3x)] dx
= (1/2)∫ cos2x dx - (1/2)∫ cos4x dx
= (1/2)(1/2)sin2x - (1/2)(1/4)sin4x + C
= (1/8)(2sin2x - sin4x) + C
sinA * sinB = (1/2)[cos(A - B) - cos(A + B)]
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