\(\int\frac{e^{6\log x}-e^{5\log x}}{e^{

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Home Questions SGK3JCR35A

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

$\int\frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx=$

Options:

$x^2+c$

$\frac{x^2}{2}+c$

$\frac{x^3}{3}+c$

$\frac{x^4}{4}+c$

Correct Answer:

$\frac{x^3}{3}+c$

Explanation:

$\int\frac{e^{6\log x}-e^{5\log x}}{e^{4\log x}-e^{3\log x}}dx=\int\frac{x^6-x^5}{x^4-x^3}dx$

$=\int\frac{x^5(x-1)}{x^3(x-1)}dx$

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