Question

若∫f’(x三次方）dx=x三次方+C 则f(x)=?

Answer 1

两边求导

f'(x³)=3x²

令a=x³

x=a^(1/3)

则f(a)=3a^(2/3)

所以f'(x)=3x^(2/3)

所以f(x)=∫3x^(2/3)dx

=3x^(2/3+1)/(2/3+1)+C

即f(x)=(9/5)x^(5/3)+C