Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:
Find $\int x\ln^2xdx$ $\ln$ denotes the logarithmic function
Options:
$x^2/2(\ln^2x-\ln x)+x^2/4+C$
$x^2/2(\ln^2x+\ln x)+x^2/2+C$
$x^2/2(\ln^2x-\ln x)-x^2/2+C$
$x^2/2(\ln^2x-2\ln x)+x^2/2+C$
Correct Answer:
$x^2/2(\ln^2x-\ln x)+x^2/4+C$
Explanation:
Do integration by parts taking $\ln^2x$ as the first and x as the second function.