Question

fx^11/(x^6+1)^100dx 这个不定积分怎么求

Answer 1

令x^6=t

原式=1/6∫t/(t+1)^100dt

=1/6∫(t+1-1)/(t+1)^100dt

=1/6∫[1/(t+1)^99-1/(t+1)^100]dt

=-1/588 (t+1)^(-98)+1/594 (t+1)^(-99)+c

=-1/588 (x^6+1)^(-98)+1/594 (x^6+1)^(-99)+c