`int_0^1(x^3-2)^2dx=?`

int_0^2(x^3+2x)dx=?

int_0^1 (x+x^2)dx

int_0^2(x^3+4x^2)dx

int_0^1(x^2)/(1+x^2)dx=?

int_0^3(4x^3+2x-3)dx=?

int_0^1(2^(2-3x))dx=?

int_0^3x^2e^(x^3)dx=?

The value of int_0^1(2x^3-3x^2-x+1)^(1/3)dx is equal to

If mgt0, ngt0 , the definite integral I=int_0^1 x^(m-1)(1-x)^(n-1)dx depends upon the values of m and n is denoted by beta(m,n) , called the beta function.For example, int_0^1 x^3 (1-x)^4dx=int_0^1 x^(4-1) (1-x)^(5-1) dx=beta(4,5) and int_0^1 x^(3/2) (1-x)^((-1)/2)dx=int_0^1 x^(5/2-1) (1-x)^(1/2-1)dx=beta(5/2,1/2) .Obviously, beta(n,m)=beta(m,n) .Now answer the question:If int_0^2 (8-x^3)^((-1)/3)dx=kbeta(1/3,2/3) , then k equals to (A) 1 (B) 1/2 (C) 1/3 (D) 1/4

int_0^1(x^2-2)/(x^2+1)dx=?