Skip to content
# Blog

## What is the integration of $\int {\frac{{{e^{6\log x}} – {e^{5\log x}}}}{{{e^{4\log x}} – {e^{3\log x}}}}} dx$~~~~~[NCERT Exemp. Q. 4,Page 163 ]

# Let $I = \int {\left( {\frac{{{e^{6\log x}} – {e^{5\log x}}}}{{{e^{4\log x}} – {e^{3\log x}}}}} \right)} dx$

# $ = \int {\left( {\frac{{{e^{\log {x^6}}} – {e^{\log {x^5}}}}}{{{e^{\log {x^4}}} – {e^{\log {x^3}}}}}} \right)} dx$

#

# [ Using log property : $e^{log_ea }=a ]$

$ = \int {\left( {\frac{{{x^6} – {x^5}}}{{{x^4} – {x^3}}}} \right)} dx$

$ = \int {\left( {\frac{{{x^3} – {x^2}}}{{x – 1}}} \right)} dx = \int {\frac{{{x^2}(x – 1)}}{{x – 1}}} dx$

$ = \int {{x^2}} dx = \frac{{{x^3}}}{3} + C$

## Buy Best Mathematics E-Books Visit : https://mathstudy.in/

## Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/

## Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/

## Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/

## Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/

$ = \int {\left( {\frac{{{x^6} – {x^5}}}{{{x^4} – {x^3}}}} \right)} dx$

$ = \int {\left( {\frac{{{x^3} – {x^2}}}{{x – 1}}} \right)} dx = \int {\frac{{{x^2}(x – 1)}}{{x – 1}}} dx$

$ = \int {{x^2}} dx = \frac{{{x^3}}}{3} + C$