Question

Which statement is most appropriate about the integral xcos (1-x)xdx? 1.It should be evaluated using Integration by Substitution because the derivative of cos(1 - x) is present in the integral. 2. It should be evaluated using Integration by Parts because the integral is a product of two functions. 3. It should be evaluated using Integration by Substitution because the derivative of (1 - x) is present in the integral. 4. It should be evaluated using Integration by Parts because the integral is a product of two different types of functions,neither of whose derivatives are present in the integral

Answer 1

it can also be written as :
\[\int\limits_{?}^{?}x^2 \cos(1-x) dx\]

so it is product of x^2 and cos(1-x) so it should be solved by parts method.