for the integration of (5x-1)^1/4 I understand that it becomes [(5x-1)^1/4]/(5/4) but I don't understand why it then needs to multiplied by 1/5. I know that you need to get from the power equalling 1/4 to 5/4, so don't you multiply by 5?

Question

for the integration of (5x-1)^1/4 I understand that it becomes [(5x-1)^1/4]/(5/4) but I don't understand why it then needs to multiplied by 1/5.  I know that you need to get from the power equalling 1/4 to 5/4, so don't you multiply by 5?

anonymous · Answer

would be from the equivalent of chain rule.

remember that the derivative of the integral of (5x -1)^1/4 is itself. so by trying to derive the result you got when you integrated, you should see why the 1/5 should be there.

you could also see it by substitution: let u = (5x + 1); du = 5 dx

anonymous · Answer

Substitution probably the easiest way.

anonymous · Answer

Because you have to do the reverse chain rule.

anonymous · Answer

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