f(x)=x^3-∫f(x)dx(积分上a,下0)a+1不=0,则∫f(x)dx(积分上a,下0)=

Question

f(x)=x^3-∫ f(x)dx(积分上a,下0) a+1不=0,则∫ f(x)dx(积分上a,下0)=

Answer 1

∫ f(x)dx(积分上a,下0)=A,
f(x)=x^3-A
A=∫ f(x)dx(积分上a,下0)=∫ (x^3-A)dx(积分上a,下0)=(1/4*x^4-Ax)(上a,下0)=1/4*a^4-Aa
A(1+a)=1/4*a^4
A=1/4*a^4 /(a+1)
即：∫ f(x)dx(积分上a,下0)=1/4*a^4 /(a+1)