1/(3x^2-2x+2)的不定积分

问题描述:

1/(3x^2-2x+2)的不定积分

1/(3x^2-2x+2)
=1/[3*(x^2-2/3*x+2/3)]
=1/3*1/[(x-1/3)^2+5/9]
原式=1/3*∫d(x-1/3)/[(x-1/3)^2+5/9]
=1/3*3/√5*arctan[(3x-1)/√5]+C
=1/√5*arctan[(3x-1)/√5]+C