Question

求(x^2)/(a^2-x^2)^(1/2)Dx的不定积分

Answer 1

x^2(a^2-x^2)^(12)

=-(a^2-x^2)^(12)+a^2(a^2-x^2)^(12)

∫x^2(a^2-x^2)^(12)dx

=-(x2)(a^2-x^2)^(12)-(a^22)arcsin(xa)+a^2arcsin(xa)+c

=(a^22)arcsin(xa)-(x2)(a^2-x^2)^(12)+C