d/dx∫x^2f(x^3)dx=?A:f(x^3)B:x^2f(x^3)C:1/3f(x)D:1/3f(x^3)

Question

d/dx∫x^2f(x^3)dx=?
A:f(x^3)
B:x^2f(x^3)
C:1/3f(x)
D:1/3f(x^3)

Answer 1

答案是B,因为积分后求导,等于原函数.可以不用计算.若要计算,则如下:先积分,∫x^2f(x^3)dx==∫f(x^3)(x^2dx)=(1/3)∫f(x^3)d(x^3)=(2/3)[f(x^3)]^2+C再求导,d/dx∫x^2f(x^3)dx==d{(2/3)[f(x^3)]^2+C}/dx=(2/3)*2f(x^3...