Let u=2−x , then −du=dx and x=2−u
Use the above substitution to evaluate the integral as,
∫x22−xdx=∫(2−u)2u(−1)du
=−∫(4+u2−4u)udu
=−∫(4u+u2u−4uu)du
=−[4(32u23)+72u27−4(52u25)]+C
=−38u23−72u27+58u25+C
=−38(2−x)23−72(2−x)27+58(2−x)25+C
Therefore, the integral is ∫x22−xdx=−38(2−x)23−72(2−x)27+58(2−x)25+C
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