A) \[{{e}^{x}}.{{x}^{5}}\]
B) \[{{e}^{x}}.{{x}^{5}}+{{e}^{x}}+C\]
C) \[{{e}^{x+1}}.{{x}^{5}}+C\]
D) \[5{{x}^{4}}.{{e}^{x}}\]
Correct Answer: B
Solution :
[b]: Let \[I=\int_{{}}^{{}}{{{e}^{x}}({{x}^{5}}+5{{x}^{4}}+1)dx}\] \[=\int_{{}}^{{}}{{{e}^{x}}({{x}^{5}}+5{{x}^{4}})dx}+\int_{{}}^{{}}{{{e}^{x}}dx}\] Now since \[\int_{{}}^{{}}{{{e}^{x}}}(f(x)+f'(x))dx={{e}^{x}}f(x)+C\] \[\therefore \]\[I={{e}^{x}}{{x}^{5}}+{{e}^{x}}+C={{e}^{x}}({{x}^{5}}+1)+C\]
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