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?

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Substitution probably the easiest way.

Because you have to do the reverse chain rule.

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