Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Preliminary Questions - Page 395: 2

The methods are: substitution, integration by parts, integration by parts, substitution.

For $\int x \cos (x^2)dx $, we can use the substitution method. For $\int x \cos (x)dx $, we can use the Integration by Parts method. For $\int x^2 e^x dx $, we can use the Integration by Parts method. For $\int x^2 e^x dx $, we can use the substitution method.