∫[(3x+1)/(4+x^2)^(1/2)]dx ∫1/[(x^2)(4-x^2)]dx

来源：学生作业帮编辑：百度作业网作业帮分类：数学作业时间：2024/07/16 08:31:25

（1）
原式=∫[3x/(4+x^2)^(1/2)]dx+∫dx/(4+x^2)^(1/2)
=3/2*∫d(4+x^2)/(4+x^2)^(1/2)+ln[x+(4+x^2)^(1/2)]+C
=3(4+x^2)^(1/2)+ln[x+(4+x^2)^(1/2)]+C
(2)
原式=1/4*∫[1/x^2+1/(4-x^2)]dx
=1/4*[∫dx/x^2+∫dx/(4-x^2)]
=1/4*[-1/x-1/4*ln|(x-2)/(x+2)|]+C
=[ln|(x+2)/(x-2)|]/16-1/4x+C

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