若∫f’(x三次方）dx=x三次方+C 则f(x)=?
问题描述：
若∫f’(x三次方）dx=x三次方+C 则f(x)=?
答
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