Can You Integrate These in A Few Seconds?

Exploiting the reverse chain rule to bypass substitution

The key to integrating these is using the Reverse Chain Rule, which I have explained here:

Integrate In Seconds: The Reverse Chain Rule

Try these for yourself before peeking at the solutions. Despite the title, and unless you have known the Reverse Chain Rule for some time, take as long as you like.

Solutions

I thought this one was a little tricky:

I hope you enjoyed reading my maths post. I have no idea when the next one will be as I write these only when I get flashes of revelation from the maths gods. If you would like to see more regular content, I always churn out a few physics stories every week. A clap and follow are much appreciated!

You can also support me directly by buying me a coffee ☕.

Walk Blimp the Dog in the Rain

Can Physics Explain Superman’s Powers?

Where does Newton’s 3rd Law come from?