A) \[\frac{-{{x}^{10}}}{2{{{{(}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
B) \[\frac{-{{x}^{5}}}{{{{{(}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
C) \[\frac{{{x}^{10}}}{2{{({{x}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
D) \[\frac{{{x}^{5}}}{2{{({{x}^{5}}+{{x}^{3}}+1)}^{2}}}+C\]
Correct Answer: C
Solution :
\[\div \]by \[{{x}^{15}}\]in Nr & Dr\[\int_{{}}^{{}}{\frac{\left( \frac{2}{{{x}^{3}}}+\frac{5}{{{x}^{6}}} \right)dx}{{{\left( 1+\frac{2}{{{x}^{2}}}+\frac{1}{{{x}^{5}}} \right)}^{3}}}}\] Let \[1+\frac{1}{{{x}^{2}}}+\frac{1}{{{x}^{5}}}=t\Rightarrow dt=-\left( \frac{2}{{{x}^{3}}}+\frac{5}{{{x}^{6}}} \right)dx\] \[\int_{{}}^{{}}{\frac{-dt}{{{t}^{3}}}=\frac{1}{2{{t}^{2}}}+c}\] where C is an arbitrary constant.
You need to login to perform this action.
You will be redirected in
3 sec
