Question

（1）积分x^3/(1+x^2)^(1/2) (2)积分（x^3+x^2+2x+1)/(x^2+1)(x^2+2)

Answer 1

1.∫x^3/(1+x^2)^(1/2) (2)

=∫[x(x^2+1)-x]/√(x^2+1)

=∫x[√(x^2+1)]-∫x/√(x^2+1)

=1/3√[(x^2+1)]^3-√(x^2+1)+c (c是实数)

2.积分（x^3+x^2+2x+1)/(x^2+1)(x^2+2)

=∫[x(x^2+2)+(x^2+1)]/(x^2+1)(x^2+2)

=∫x/(x^2+1)+∫1/(x^2+2)

=arctanX+√2/2arctan(√2x/2)+c (c是实数)