Evaluate the indefinite integral. (Use C for the constant of integration.)?

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1 Answer
Nov 16, 2017

The integral equals #3/8(z^4 + 7)^(2/3) + C#

Explanation:

We let #u = z^4 + 7#. Then #du = 4z^3 dz# and #dz= (du)/(4z^3)#.

#I = int z^3/root(3)(u) * (du)/(4z^3)#

#I = 1/4int 1/u^(1/3) du#

#I = 1/4int u^(-1/3) du#

#I = 1/4(3/2)u^(2/3)#

#I = 3/8u^(2/3)#

#I = 3/8(z^4 + 7)^(2/3)+ C#

Hopefully this helps!