La integral de[ V?

<img src="https://tex.z-dn.net/?f=%20%5Cint%20%7Bv%284v%20%5E%7B2%7D%2B2%29%5E%7B5%7D%20%7D%20%5C%2C%20dv%20%3D%20%5Cint%20%7B%284v%20%5E%7B2%7D%2B2%29%5E%7B5%7D%20%7D%20%5C%2C%20vdv%20" /> (1)

Cambio de variable

<img src="https://tex.z-dn.net/?f=w%3D4v%20%5E%7B2%7D%2B2" />

<img src="https://tex.z-dn.net/?f=dw%3D8vdv" />

<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bdw%7D%7B8%7D%3Dvdv" />

<img src="https://tex.z-dn.net/?f=%20vdv%3D%5Cfrac%7Bdw%7D%7B8%7D" /> (2)

(2)en (1)

<img src="https://tex.z-dn.net/?f=%5Cint%20%7B%284v%20%5E%7B2%7D%2B2%29%5E%7B5%7D%20%7D%20%5C%2C%20vdv%20" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%7B%28w%29%5E%7B5%7D%20%7D%20%5C%2C%5Cfrac%7Bdw%7D%7B8%7D%20" />

<img src="https://tex.z-dn.net/?f=%5Cint%20%7Bw%5E%7B5%7D%20%7D%20%5C%2C%5Cfrac%7Bdw%7D%7B8%7D" />

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D.%5Cfrac%7B1%7D%7B%285%2B1%29%7D%20w%5E%7B5%2B1%7D%2BC" />

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7D.%5Cfrac%7B1%7D%7B6%7D%20w%5E%7B6%7D%2BC" />

[img = 10]

Deshaciendo el cambio →w = 4v ^ {2} + 2

[img = 11]

[img = 12]

Espero te sea de utilidad.

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