Question

∫x^5/(1+x^2)怎么算

Answer 1

x^5/(1+x^2)=[x(1+x^2)^2-2x^3-x]/(1+x^2)=x(1+x^2)-(2x^3+x)/(1+x^2)=x+x^3-[2x(x^2+1)-x]/(1+x^2)

=x+x^3-2x+x/(1+x^2)=(1/4)(x^4)'-(1/2)(x^2)'-(1/2)(x^2+1)'/(1+x^2)

∫x^5/(1+x^2)dx=x^4/4-x^2/2-ln(1+x^2)/2+C