丿1/(sin^2x+2cos^2x)dx不定积分求过 程

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丿1/(sin^2x+2cos^2x)dx不定积分求过 程
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丿1/(sin^2x+2cos^2x)dx不定积分求过 程
丿1/(sin^2x+2cos^2x)dx不定积分求过 程

丿1/(sin^2x+2cos^2x)dx不定积分求过 程
原式=∫1/(1+(cosx)^2) dx 分子分母同除以(cosx)^2
=∫(secx)^2/((secx)^2+1) dx
=∫1/((secx)^2+1) d (tanx)
=∫1/((tanx)^2+2) d (tanx)
套公式
=1/√2*arctan((tanx)/√2)+C

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