U-substitution integration help

[emmi1717]

Hello! I have a math problem that looks like:



I understand that I need to use u-substitution. My u is cot(5x), which makes my du -csc²x(5x).

I thought that this would get me ∫-u⁶du

But, on my answer key, the next step looks like:


I have no idea where the 5 in the denominator came from! Could someone explain why you have to put a 5 there? I'm sure this is a really simple thing, but I can't figure it out!

 

[Dr.Peterson]

My u is cot(5x), which makes my du -csc2x(5x).

Check your differentiation. I think you forgot about the chain rule. (You also omitted dx, but that's less important.)

 

[emmi1717]

Thank you so much! I did forget about the chain rule.