1. Tardigrade
  2. Question
  3. Mathematics
  4. ∫(e6 log ex-e5 log ex/e4 log ex-e3 log ex)dx is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $ \int{\frac{{{e}^{6{{\log }_{e}}x}}-{{e}^{5{{\log }_{e}}x}}}{{{e}^{4{{\log }_{e}}x}}-{{e}^{3{{\log }_{e}}x}}}}dx $ is equal to

KEAMKEAM 2009

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 $