Question

X^3/根号下(1+x^2)的原函数,

Answer 1

X^3/根号下(1+x^2)的原函数=∫[x^3/(√1+x^2)]dx

=1/2∫[x^2/(√1+x^2)]d(x^2)

=1/2∫[(x^2+1-1)/(√1+x^2)]d(x^2)

=1/2∫(√1+x^2)d(x^2+1)-1/2∫[1/(√1+x^2)](d(x^2+1)

=1/2[(2/3)(x^2+1)^(3/2)-2(√1+x^2)]

=(x^2-2)(√1+x^2)/3