(x方加2)分之一的不定积分
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∫[ x^2/(x^2+2)] dx
=∫[ 1 - 2/(x^2+2)] dx
= x -2∫ dx/(x^2+2)
let
x= √2 tany
dx =√2 (secy)^2 dy
∫ dx/(x^2+2)
=(√2/2)∫ dy
=(√2/2)y + C'
=(√2/2)arctan(x/√2) + C'
∫[ x^2/(x^2+2)] dx
= x -2∫ dx/(x^2+2)
= x -√2arctan(x/√2) + C
=∫[ 1 - 2/(x^2+2)] dx
= x -2∫ dx/(x^2+2)
let
x= √2 tany
dx =√2 (secy)^2 dy
∫ dx/(x^2+2)
=(√2/2)∫ dy
=(√2/2)y + C'
=(√2/2)arctan(x/√2) + C'
∫[ x^2/(x^2+2)] dx
= x -2∫ dx/(x^2+2)
= x -√2arctan(x/√2) + C
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