求不定积分:积分号dx/根号下(1+x-x^2)

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求不定积分:积分号dx/根号下(1+x-x^2)求不定积分:积分号dx/根号下(1+x-x^2)求不定积分:积分号dx/根号下(1+x-x^2)∫dx/√(1+x-x^2)=∫dx/[5/4-(x-1

求不定积分:积分号dx/根号下(1+x-x^2)
求不定积分:积分号dx/根号下(1+x-x^2)

求不定积分:积分号dx/根号下(1+x-x^2)
∫dx/√(1+x-x^2)
=∫dx/[5/4-(x-1/2)^2]
=4/5·∫dx/[1-(√5/2·x-√5/2)^2]
=4/5·2/√5·∫d(√5/2·x)/[1-(√5/2·x-√5/2)^2]
=8√5/25·arcsin(√5/2·x)+C

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