不要慌,根号就是1/2次方.∫√xdx=∫x^(1/2)dx=2/3*x^(3/2)+c,d√x/dx=1/2*x^(-1/2)=1/(2√x)
∫[x*√(5+x^2)]dx
=1/2*∫[√(5+x^2)]dx^2+c
=1/2*∫[(5+t)^(1/2)]dt+c
=1/2*2/3*(5+t)^(3/2)+c
=1/3*(5+x^2)^(3/2)+c
d√(5+x^2)/dx=2x*(1/2)*(5+x^2)^(-1/2)=x/√(5+x^2)