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不定积分一题求∫dx/(2+sinx-2cosx)

2012-10-28 11:23:313***
求∫dx/(2+sinx-2cosx)不定积分一题求∫dx/(2+sinx-2cosx):解:2+sinx-2cosx=2(1-cosx)+sinx=4sin²(x/2)+2sin(x/2?

最佳回答

  • 解:2+sinx-2cosx=2(1-cosx)+sinx=4sin²(x/2)+2sin(x/2)cos(x/2) `∫dx/(2+sinx-2cosx) =∫dx/[4sin²(x/2)+2sin(x/2)cos(x/2)] =∫d[2tan(x/2)]/{2tan(x/2)[2tan(x/2)+1] =∫{1/2tan(x/2)-1/[2tan(x/2)+1]}d[2tan(x/2)] =ln|2tan(x/2)/[2tan(x/2)+1]|+C
    2012-10-28 11:38:40
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