Looking on the internet deeply has found these results:

He is busy to do homework is the most popular phrase on the web.

He is busy doing homework 113,800 results on the web	He is busy to do homework 16,870,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
He is busy with affairs of state. He's probably doing homework or something. He is busy campaigning and canvassing the neighborhood. He is busy with affairs of state. He is busy with his homework now. Missus, Nucky wishes to say he is busy tonight. I'm busy doing John's homework. He is busy with that Eva business.	Missus, Nucky wishes to say he is busy tonight. I'M SURE YOU'RE BUSY WITH YOUR HOMEWORK AND SO FORTH BUT I GOT SOME REALLY GOOD NEWS She's probably too busy complaining about her homework. He is busy campaigning and canvassing the neighborhood. I'm busy doing John's homework. He is busy with his homework now. He is busy with that Eva business. Here in New York, security is busy to continue the preparations for funeral U.S. vice president.

He is busy doing homework

113,800 results on the web

He is busy to do homework

16,870,000 results on the web

More popular!

Missus, Nucky wishes to say he is busy tonight.
I'M SURE YOU'RE BUSY WITH YOUR HOMEWORK AND SO FORTH BUT I GOT SOME REALLY GOOD NEWS
She's probably too busy complaining about her homework.
He is busy campaigning and canvassing the neighborhood.
I'm busy doing John's homework.
He is busy with his homework now.
He is busy with that Eva business.
Here in New York, security is busy to continue the preparations for funeral U.S. vice president.