Find the value of `int (x^2 dx)/(1+x^6)`

Find the value of int_0^1x(1-x)dx

Find the value of " int x sec^(2)x dx

Find the value of int dx/((x -1)sqrt(x^2 + 4))

find the value of int((x^3+8)(x-1))/(x^2-2x+4)dx

If int_0^1e^ (-x^2) dx=a , then find the value of int_0^1x^2e^ (-x^2) dx in terms of a .

Evaluate: int(dx)/(sqrt((x-1)(2-x))) by the substitution x=1+sin^(2)theta . Hence, find the value of int_(1)^(2)(dx)/(sqrt((x-1)(2-x)))

Find the value of int_(1/2)^(2)e^(|x-1/x|)dx .

Find the value of int_(0)^(1){(sin^(-1)x)//x}dx .

Find the value of int_(0)^(1)root(3)(2x^(3)-3x^(2)-x+1)dx .