Question

求不定积分,希望有详解,

Answer 1

∫ 4 /(4x+x^3) dx

= ∫ [ 1/x - x/(4+x^2) ] dx

= ∫ 1/x dx - ∫ x / (4+x^2) dx

= ln|x| - 1/2 ∫ 1/(4+x^2) d(4+x^2)

= ln|x| - 1/2 ln(4+x^2) + C

= 1/2 ln[ x^2 /(4+x^2) ] +C

满意请好评o(∩_∩)o