How to integrate root (8 x^6) dx from 2 to 0

Please explain in a multi step format

Thanks!

A single term inside a root can be broken up like this
root(8)*root(x^6)

A square root is just a power of 1/2
root(8)*(x^6)^1/2

A power within a power can just be multiplied
root(8)*x^3

Split the root(8) like we split the original root (8 = 2*4)
root(4)*root(2)*x^3
=2root(2)*x^3

Integrate!
Int[2root(2)*x^3]dx
=2root(2) * Int[x^3]dx
=2root(2) * (x^4)/4 + C

To find the definite integral substitute the terminals into this result subtract the lower terminal result from the upper terminal result. Don't worry about the constant.

=2root(2) * (2^4)/4 - 2root(2) * (0^4)/4
=2root(2) * 16/4
=8root(2)

hint: √(8 x^6) = √8 * |x^3| and on the interval you are integrating, x > 0 so it simplifies to √8 * x^3