Question

（x5+1)/(x2+1)对x的不定积分

Answer 1

(x^5 +1)/(x²+1)

=(x^5+x³-x³-x+x+1)/(x²+1)

=[x³(x²+1)-x(x²+1)+x+1]/(x²+1)

=x³ -x +x/(x²+1) +1/(x²+1)

∫[(x^5 +1)/(x²+1)]dx

=∫[x³ -x +x/(x²+1) +1/(x²+1)]dx

=x⁴/4 -x²/2 +(1/2)ln(x²+1) +arctan(x) +C