A) \[\frac{{{x}^{3}}}{3}+c\]
B) \[\frac{{{x}^{2}}}{2}+c\]
C) \[\frac{{{x}^{2}}}{3}+c\]
D) \[\frac{-{{x}^{3}}}{3}+c\]
E) \[x+c\]
Correct Answer: A
Solution :
\[I=\int{\frac{{{e}^{6{{\log }_{e}}x}}-{{e}^{-5{{\log }_{e}}x}}}{{{e}^{4{{\log }_{e}}x}}-{{e}^{3{{\log }_{e}}x}}}}dx\] \[=\int{\frac{{{x}^{6}}-{{x}^{5}}}{{{x}^{4}}-{{x}^{3}}}}dx=\int{\frac{{{x}^{5}}(x-1)}{{{x}^{3}}(x-1)}}dx\] \[=\int{{{x}^{2}}dx}=\frac{{{x}^{3}}}{3}+c\]
You need to login to perform this action.
You will be redirected in
3 sec
