`int_0^1 x(root(3)(x) + root(4)(x)) dx` Evaluate the integral

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You need to evaluate the definite integral, such that:

`int_0^1 x(root(3) x + root(4) x)dx = int_0^1 (x^(1+1/3) + x^(1+1/4))dx`

`int_0^1 x(root(3) x + root(4) x)dx = ((x^(2+1/3))/(2+1/3) + (x^(2+1/4))/(2+1/4))|_0^1`

`int_0^1 x(root(3) x + root(4) x)dx = ((3/7)x^2root(3)x + (4/9)x^2root(4)x)|_0^1`

`int_0^1 x(root(3) x + root(4) x)dx = 3/7 + 4/9`

`int_0^1 x(root(3) x + root(4) x)dx = 55/63`

Hence, evaluating the definite integral yields

`int_0^1 x(root(3) x + root(4) x)dx = 55/63.`

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