A) \[-\frac{1}{2}\]
B) \[\frac{1}{2}\]
C) \[-\frac{1}{4}\]
D) \[\frac{1}{4}\]
Correct Answer: D
Solution :
\[\int{\frac{5{{x}^{8}}+7{{x}^{6}}}{{{({{x}^{2}}+1+2{{x}^{7}})}^{2}}}dx}=\int{\frac{5{{x}^{-\,6}}+7{{x}^{-\,8}}}{{{\left( \frac{1}{{{x}^{7}}}+\frac{1}{{{x}^{5}}}+2 \right)}^{2}}}dx}\] |
\[=\,\frac{1}{2+\frac{1}{{{x}^{5}}}+\frac{1}{{{x}^{7}}}}+C\] |
As \[f(0)-0,\] \[f(x)=\frac{{{x}^{7}}}{2{{x}^{7}}+{{x}^{2}}+1}\] |
\[f(1)=\frac{1}{4}.\] |
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