x²/(a的6次方-x的6次方)的不定积分

x²/(a的6次方-x的6次方)的不定积分
x²/(a的6次方-x的6次方)的不定积分

x²/(a的6次方-x的6次方)的不定积分
∫x^2dx/[a^6-x^6]
=(1/3)∫[a^3-x^3+a^3+x^3]dx^3/[2a^3 *(a^3-x^3)(a^3+x^3)]
=(1/(6a^3)) [ ∫d(x^3+a^3)/(x^3+a^3)+∫d(x^3-a^3)/a^3-x^3)]
=(1/(6a^3))ln|a^3+x^3|/|a^3-x^3|+C