Recurrence integration by parts - integrating cotx (1 Viewer)

[gamja]

I'm going to take a while to do latex so here's a picture of my working so far instead:

I don't know how to work the integral on the last step.

Maybe some hints? (use spoilers)
Thanks so much for the help!

 

[tywebb]

You can use the wolframalpha app with the show steps function and I get this for part a:






Quicker than typing it up myself.

So it's just repeated use of the reduction formula except for the last few steps.

Similar thing for part b and then the answer is (ln4-1)/4. See if you can do it and let me know if you want the show steps from wolframalpha app.

 

[gamja]

isn't showing steps behind a paywall for 'pro' pricing plan on wolfram?

 

[tywebb]

isn't showing steps behind a paywall for 'pro' pricing plan on wolfram?

I think it is that way for the website. But I used the app on my ipad and that doesn't require a subscription.

Anyway I googled the proof of the formula itself and found this:


Again googling was quicker than typing it up myself.