Using substitution : calculate the following integral (x^3+2)^3/5 . x^5 dx?

Using substitution : calculate the following integral (x^3+2)^3/5 . x^5 dx?
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Let z=x^3+2, then dz=3x^2dx. The integral becomes: ∫z^(3/5)x^5.dz/(3x^2)=∫z^(3/5)x^3dz/3=∫z^(3/5)(z-2)dz/3.

This becomes ∫((z^(8/5)-2z^(3/5))/3)dz=((5/13)z^(13/5)-(5/4)z^(8/5))/3+c (c is constant of integration).

Replacing z: (5/156)(4(x^3+2)^(13/5)-13(x^3+2)^(8/5)+c=(5/156)(x^3+2)^(8/5)(4x^3-5)+c.
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