(a^2+x^2)/a+x的原函数怎么求
2个回答

∫[(a^2+x^2)/(a+x)]dx

=∫{[(a^2+2ax+x^2)-2ax]/(a+x)}dx

=∫{[(a+x)^2-2ax]/(a+x)}dx

=∫(a+x)dx-2a∫[x/(a+x)]dx

=(1/2)(a+x)^2-2a∫{[(a+x)-a]/(a+x)}dx

=(1/2)(a+x)^2-2a∫dx+2a^2∫[1/(a+x)]dx

=(1/2)(a+x)^2-2ax+[2a^2]ln(a+x)+C.