I mean, it's definitely
possible that this was a mistake on your teacher's behalf. But, I, an anonymous stranger on the internet that knows neither you, nor your teacher, nor even what school you attend, cannot say with any degree of certainty. Only your teacher can say for certain. My best guess, however, is that it's a genuine problem. It's a bit ugly and has a lot of terms, but it's not excessively awful. When you get integrals that look deceptively simple like \(\displaystyle \displaystyle \int cos(x^2) \: dx\), whose solution actually involves a
Fresnel Integral, or \(\displaystyle \displaystyle \int x! \: dx\), to which WolframAlpha says only "(no result found in terms of standard mathematical functions)," then you can suspect the exercise might be a typo
Mostly, though, this problem is just busy work. Expanding out the \(\displaystyle (x - 5)^{11}\) term can be made a bit less tedious by using the
Binomial Theorem and Pascal's Triangle, and then the lingering x out front increases the degree of the resulting polynomial by 1. When all is said and done, you'll have a 12th degree polynomial which can be broken up into 12 easy integrals via the sum rule.
