A) \[\frac{1}{20}{{({{x}^{2}}+6x+10)}^{10}}+c\]
B) \[\frac{1}{20}{{(x+3)}^{2}}{{({{x}^{2}}+6x+10)}^{10}}+c\]
C) \[\frac{1}{16}{{({{x}^{2}}+6x+10)}^{8}}+c\]
D) \[\frac{1}{38}{{(x+3)}^{19}}+\frac{1}{2}(x+3)+c\]
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{(x+3){{({{x}^{2}}+6x+10)}^{9}}dx}\] \[=\frac{1}{2}\int_{{}}^{{}}{(2x+6){{({{x}^{2}}+6x+10)}^{2}}dx}\] \[=\frac{1}{2}\frac{{{({{x}^{2}}+6x+10)}^{10}}}{10}+c\]\[=\frac{1}{20}{{({{x}^{2}}+6x+10)}^{10}}+c\].
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